Relevant bibliographies by topics / Mean curvature operator

Academic literature on the topic 'Mean curvature operator'

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Published: 9 March 2023
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Journal articles on the topic "Mean curvature operator"

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Mawhin, Jean. "Nonlinear boundary value problems involving the extrinsic mean curvature operator." Mathematica Bohemica 139, no. 2 (2014): 299–313. http://dx.doi.org/10.21136/mb.2014.143856.

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Bessa, Gregório P., Luquésio P. Jorge, Barnabé P. Lima, and José F. Montenegro. "Fundamental tone estimates for elliptic operators in divergence form and geometric applications." Anais da Academia Brasileira de Ciências 78, no. 3 (September 2006): 391–404. http://dx.doi.org/10.1590/s0001-37652006000300001.

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We establish a method for giving lower bounds for the fundamental tone of elliptic operators in divergence form in terms of the divergence of vector fields. We then apply this method to the Lr operator associated to immersed hypersurfaces with locally bounded (r + 1)-th mean curvature Hr + 1 of the space forms Nn+ 1(c) of constant sectional curvature c. As a corollary we give lower bounds for the extrinsic radius of closed hypersurfaces of Nn+ 1(c) with Hr + 1 > 0 in terms of the r-th and (r + 1)-th mean curvatures. Finally we observe that bounds for the Laplace eigenvalues essentially bound the eigenvalues of a self-adjoint elliptic differential operator in divergence form. This allows us to show that Cheeger's constant gives a lower bounds for the first nonzero Lr-eigenvalue of a closed hypersurface of Nn+ 1(c).
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Yang, Dan, and Yu Fu. "Biharmonic hypersurfaces in pseudo-Riemannian space forms." International Journal of Geometric Methods in Modern Physics 13, no. 07 (July 25, 2016): 1650094. http://dx.doi.org/10.1142/s0219887816500948.

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Let [Formula: see text] be a nondegenerate biharmonic pseudo-Riemannian hypersurface in a pseudo-Riemannian space form [Formula: see text] with constant sectional curvature [Formula: see text]. We show that [Formula: see text] has constant mean curvature provided that it has three distinct principal curvatures and the Weingarten operator can be diagonalizable.
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Harrell II, Evans M., and Michael Loss. "On the Laplace Operator Penalized by Mean Curvature." Communications in Mathematical Physics 195, no. 3 (August 1998): 643–50. http://dx.doi.org/10.1007/s002200050406.

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DE LIMA, HENRIQUE FERNANDES, ANTONIO FERNANDO DE SOUSA, and MARCO ANTONIO LÁZARO VELÁSQUEZ. "STABILITY OF SPACELIKE HYPERSURFACES WITH HIGHER-ORDER MEAN CURVATURES LINEARLY RELATED IN CONFORMALLY STATIONARY SPACETIMES." International Journal of Mathematics 24, no. 14 (December 2013): 1350109. http://dx.doi.org/10.1142/s0129167x13501097.

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In this paper, we establish the notion of (r, s)-stability concerning spacelike hypersurfaces with higher-order mean curvatures linearly related in conformally stationary spacetimes of constant sectional curvature. In this setting, we characterize (r, s)-stable closed spacelike hypersurfaces through the analysis of the first eigenvalue of an operator naturally attached to the higher-order mean curvatures. Moreover, we obtain sufficient conditions which assure the (r, s)-stability of complete spacelike hypersurfaces immersed in the de Sitter space.
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Matsutani, Shigeki. "A constant mean curvature surface and the Dirac operator." Journal of Physics A: Mathematical and General 30, no. 11 (June 7, 1997): 4019–29. http://dx.doi.org/10.1088/0305-4470/30/11/028.

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Etemad, A. "First eigenvalue of the Laplace operator and mean curvature." Ukrainian Mathematical Journal 60, no. 7 (July 2008): 1172–75. http://dx.doi.org/10.1007/s11253-008-0111-y.

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Yang, Dan, Jinchao Yu, Jingjing Zhang, and Xiaoying Zhu. "A class of hypersurfaces in $ \mathbb{E}^{n+1}_{s} $ satisfying $ \Delta \vec{H} = \lambda\vec{H} $." AIMS Mathematics 7, no. 1 (2022): 39–53. http://dx.doi.org/10.3934/math.2022003.

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<abstract><p>A nondegenerate hypersurface in a pseudo-Euclidean space $ \mathbb{E}^{n+1}_{s} $ is called to have proper mean curvature vector if its mean curvature $ \vec{H} $ satisfies $ \Delta \vec{H} = \lambda \vec{H} $ for a constant $ \lambda $. In 2013, Arvanitoyeorgos and Kaimakamis conjectured <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>: any hypersurface satisfying $ \Delta \vec{H} = \lambda \vec{H} $ in pseudo-Euclidean space $ \mathbb E_{s}^{n+1} $ has constant mean curvature. This paper will give further support evidences to this conjecture by proving that a linear Weingarten hypersurface $ M^{n}_{r} $ in $ \mathbb E^{n+1}_{s} $ satisfying $ \Delta \vec{H} = \lambda \vec{H} $ has constant mean curvature if $ M^{n}_{r} $ has diagonalizable shape operator with less than seven distinct principal curvatures.</p></abstract>
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Ecker, Klaus. "On mean curvature flow of spacelike hypersurfaces in asymptotically flat spacetimes." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 55, no. 1 (August 1993): 41–59. http://dx.doi.org/10.1017/s1446788700031918.

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AbstractWe prove a priori estimates for the gradient and curvature of spacelike hypersurfaces moving by mean curvature in a Lorentzian manifold. These estimates are obtained under much weaker conditions than have been previously assumed. We also use mean curvature flow in the construction of maximal slices in asymptotically flat spacetimes. An essential tool is a maximum principle for sub-solutions of a parabolic operator on complete Riemannian manifolds with time-dependent metric.
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Qi, Xuesen, and Ximin Liu. "Evolution of the first eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow." Open Mathematics 18, no. 1 (January 1, 2020): 1518–30. http://dx.doi.org/10.1515/math-2020-0090.

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Abstract In this paper, we discuss the monotonicity of the first nonzero eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow (MCF). By imposing conditions associated with the mean curvature of the initial hypersurface and the coefficient function of the forcing term of a forced MCF, and some special pinching conditions on the second fundamental form of the initial hypersurface, we prove that the first nonzero closed eigenvalues of the Laplace operator and the p-Laplace operator are monotonic under the forced MCF, respectively, which partially generalize Mao and Zhao’s work. Moreover, we give an example to specify applications of conclusions obtained above.
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Dissertations / Theses on the topic "Mean curvature operator"

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COLOMBO, GIULIO. "GLOBAL GRADIENT BOUNDS FOR SOLUTIONS OF PRESCRIBED MEAN CURVATURE EQUATIONS ON RIEMANNIAN MANIFOLDS." Doctoral thesis, Università degli Studi di Milano, 2021. http://hdl.handle.net/2434/813095.

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This thesis is concerned with the study of qualitative properties of solutions of the minimal surface equation and of a class of prescribed mean curvature equations on complete Riemannian manifolds. We derive global gradient bounds for non-negative solutions of such equations on manifolds satisfying a uniform Ricci lower bound and we obtain Liouville-type theorems and other rigidity results on Riemannian manifolds with non-negative Ricci curvature. The proof of the aforementioned global gradient bounds for non-negative solutions u is based on the application of the maximum principle to an elliptic differential inequality satisfied by a suitable auxiliary function z=f(u,|Du|), in the spirit of Bernstein’s method of a priori estimates for nonlinear PDEs and of Yau’s proof of global gradient bounds for harmonic functions on complete Riemannian manifolds. The particular choice of the auxiliary function z parallels the one in Korevaar’s proof of a priori gradient estimates for the prescribed mean curvature equation in Euclidean space. The rigidity results obtained in the last part of the thesis include a Liouville theorem for positive solutions of the minimal surface equation on complete Riemannian manifolds with non-negative Ricci curvature, a splitting theorem for complete parabolic manifolds of non-negative sectional curvature supporting non-constant solutions with linear growth of the minimal surface equation, and a splitting theorem for domains of complete parabolic manifolds with non-negative Ricci curvature supporting non-constant solutions of overdetermined problems involving the mean curvature operator.
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Cárdenas, Carlos Wilson Rodríguez. "Genericity of bumpy metrics, bifurcation and stability in free boundary CMC hypersurfaces." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-15022019-111803/.

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In this thesis we prove the genericity of the set of metrics on a manifold with boundary M^{n+1}, such that all free boundary constant mean curvature (CMC) embeddings \\varphi: \\Sigma^n \\to M^{n+1}, being \\Sigma a manifold with boundary, are non-degenerate (Bumpy Metrics), (Theorem 2.4.1). We also give sufficient conditions to obtain a free boundary CMC deformation of a CMC inmersion (Theorems 3.2.1 and 3.2.2), and a stability criterion for this type of immersions (Theorem 3.3.3 and Corollary 3.3.5). In addition, given a one-parametric family, {\\varphi _t : \\Sigma \\to M} , of free boundary CMC immersions, we give criteria for the existence of smooth bifurcated branches of free boundary CMC immersions for the family {\\varphi_t}, via the implicit function theorem when the kernel of the Jacobi operator J is non-trivial, (Theorems 4.2.3 and 4.3.2), and we study stability and instability problems for hypersurfaces in this bifurcated branches (Theorems 5.3.1 and 5.3.3).
Nesta tese, provamos a genericidade do conjunto de métricas em uma variedade com fronteira M^{n+1}, de modo que todos os mergulhos de curvatura média constante (CMC) e fronteira livre \\varphi : \\Sigma^n \\to M^{n+1}, sendo \\Sigma uma variedade com fronteira, sejam não-degenerados (Métricas Bumpy), (Teorema 2.4.1). Nós também fornecemos condições suficientes para obter uma deformação CMC e fronteira livre de uma imersão CMC (Teoremas 3.2.1 and 3.2.2), e um critério de estabilidade para este tipo de imersões (Teorema 3.3.3 and Corolario 3.3.5). Além disso, dada uma família 1-paramétrica, {\\varphi _t : \\Sigma \\to M} , de imersões de CMC e fronteira livre, damos os critérios para a existência de ramos de bifurcação suaves de imersões CMC e fronteira livre para a familia {\\varphi_t}, por meio de o teorema da função implícita quando o kernel do operador Jacobi J é não-trivial, (Teoremas 4.2.3 and 4.3.2), e estudamos o problema da estabilidade e instabilidade para hipersuperfícies em naqueles ramos de bifurcação (Teoremas 5.3.1 and 5.3.3).
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Derlet, Ann. "Eigenvalues of the p-Laplacian in population dynamics and nodal solutions of a prescribed mean curvature problem." Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209932.

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Cette thèse est consacrée à l'étude de plusieurs problèmes d'équations aux dérivées partielles non-linéaires.

La première partie (chapitres 1-2-3) traite d'un problème trouvant son origine en biologie mathématique, à savoir l'étude de la survie à long terme d'une population dont l'évolution est gouvernée par une équation parabolique non-linéaire. Dans le modèle considéré, le mécanisme de diffusion est contrôlé par le p-Laplacien, la non-linéarité est de type logistique et fait intervenir un poids m pouvant changer de signe, et les conditions aux limites sont de flux nul. Le poids m correspond à une répartition des ressources devant permettre la survie de la population. Dans le chapitre 1, nous déterminons entre autres un critère de survie à long terme faisant intervenir la valeur propre principale du p-Laplacien avec poids m. Cette valeur propre apparait, plus précisément, comme la valeur limite d'un paramètre en-dessous de laquelle toute solution positive de l'équation converge vers zéro lorsque t tend vers l'infini. Ceci nous conduit naturellement au problème de minimiser la valeur propre en question lorsque m varie dans une classe adéquate de poids. Dans le chapitre 2, nous prouvons l'existence de minimiseurs et montrons que ces derniers satisfont une propriété de type “bang-bang”. Plusieurs propriétés de montonie sont aussi étudiées dans des situations géométriques particulières, et une caractérisation complète est donnée en dimension 1. Le chapitre 3 est consacré à l'élaboration de simulations numériques, où l'algorithme utilisé combine un méthode de plus grande pente avec une représentation de certains ensembles comme ensembles de niveaux.

La deuxième sujet de cette thèse (chapitre 4) est un problème elliptique faisant intervenir l'opérateur de courbure moyenne. Nous nous intéressons à l'existence et à la multiplicité de solutions nodales de ce problème. Nous montrons que, si un certain paramètre de l'équation est suffisamment grand, il existe une solution nodale qui change de signe exactement deux fois. Nous établissons également l'existence d'un nombre arbitrairement grand de solutions nodales. Enfin, dans le cas particulier où le domaine est une boule, un résultat de brisure de symétrie est obtenu, résultat qui induit l'existence d'au moins deux solutions à deux domaines nodaux.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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Monte, Luiz AntÃnio Caetano. "Espectro essencial de uma classe de variedades riemannianas." Universidade Federal do CearÃ, 2012. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=9185.

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Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior
Neste trabalho, provaremos alguns resultados sobre espectro essencial de uma classe de variedades Riemannianas, nÃo necessariamente completas, com condiÃÃes de curvatura na vizinhanÃa de um raio. Sobre essas condiÃÃes obtemos que o espectro essencial do operador de Laplace contÃm um intervalo. Como aplicaÃÃo, obteremos o espectro do operador de Laplace de regiÃes ilimitadas dos espaÃos formas, tais como a horobola do espaÃo hiperbÃlico e cones do espaÃo Euclidiano. Construiremos tambÃm um exemplo que indica a necessidade das condiÃÃes globais sobre o supremo das curvaturas seccionais fora de uma bola para que a variedade nÃo tenha espectro essencial.
In this thesis we consider a family of Riemannian manifolds, not necessarily complete, with curvature conditions in a neighborhood of a ray. Under these conditions we obtain that the essential spectrum of the Laplace operator contains an interval. The results presented in this thesis allow to determine the spectrum of the Laplace operator on unlimited regions of space forms, such as horoball in hyperbolic space and cones in Euclidean space. Also construct an example that shows the need of global conditions on the supreme sectional curvature outside a ball, so that the variety has no essential spectrum.
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Ramos, Álvaro Krüger. "Constant mean curvature hypersurfaces on symmetric spaces, minimal graphs on semidirect products and properly embedded surfaces in hyperbolic 3-manifolds." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/118222.

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Provamos resultados sobre a geometria de hipersuperfícies em diferentes espaços ambiente. Primeiro, definimos uma aplicação de Gauss generalizada para uma hipersuperfície Mn-1 c/ Nn, onde N é um espaço simétrico de dimensão n ≥ 3. Em particular, generalizamos um resultado de Ruh-Vilms e apresentamos aplicações. Em seguida, estudamos superfícies em espaços de dimensão 3: estudamos a equação da curvatura média em um produto semidireto R2oAR e obtemos estimativas da altura e a existência de gráficos mínimos do tipo Scherk. Finalmente, no espaço ambiente de uma variedade hiperbólica de dimensão 3: nós apresentamos condições suficientes para que um mergulho completo de uma superfície ∑ de topologia finita em N com curvatura média |H∑| ≤ 1 seja próprio.
We prove results concerning the geometry of hypersurfaces on di erent ambient spaces. First, we de ne a generalized Gauss map for a hypersurface Mn-1 c/ Nn, where N is a symmetric space of dimension n ≥ 3. In particular, we generalize a result due to Ruh-Vilms and make some applications. Then, we focus on surfaces on spaces of dimension 3: we study the mean curvature equation of a semidirect product R2 oA R to obtain height estimates and the existence of a Scherk-like minimal graph. Finally, on the ambient space of a hyperbolic manifold N of dimension 3 we give su cient conditions for a complete embedding of a nite topology surface ∑ on N with mean curvature |H∑| ≤ 1 to be proper.
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McCoy, James A. (James Alexander) 1976. "The surface area preserving mean curvature flow." Monash University, Dept. of Mathematics, 2002. http://arrow.monash.edu.au/hdl/1959.1/8291.

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Castillon, Philippe. "Sur les sous-variétés à courbure moyenne constante dans l'espace hyperbolique." Université Joseph Fourier (Grenoble), 1997. http://www.theses.fr/1997GRE10006.

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Dans les chapitres 2 et 3 de cette these, on s'interesse aux sous-varietes de l'espace hyperbolique dont la courbure moyenne est constante et strictement inferieure a un. Le premier resultat qu'on obtient concerne l'operateur de stabilite. Dans notre cas, cet operateur est essentiellement auto-adjoint, et on connait un minorant positif de son spectre essentiel. On montre que le nombre de valeurs propres inferieures a ce minorant est fini, et on en obtient un majorant qui fait intervenir la courbure totale. Ce faisant, on obtient un majorant de l'indice de morse de sous-variete. Un des points importants de la preuve est de controler le noyau de la chaleur de la sous-variete. On obtient ce controle en montrant qu'on a sur la sous-variete des inegalites isoperimetriques. Le second resultat porte sur la compactification. On etend aux sous-varietes a courbure moyenne constantes un resultat de g. De oliveira pour les sous-varietes minimales: on montre que la sous-variete est diffeomorphe a l'interieur d'une variete compact a bord, et que l'immersion s'etend continument au bord en une application a valeurs dans le compactifie de l'espace hyperbolique. Dans le chapitre 4, on etudie les surfaces de revolution a courbure moyenne constante dans l'espace hyperbolique. On obtient une construction cinematique de leurs meridiennes analogue a celle donne par c. Delaunay dans l'espace euclidien. Les courbes a faire rouler ont des proprietes focales similaires a celles des coniques euclidiennes. On trouve les analogues hyperboliques des ellipses, des hyperboles ainsi qu'une surprenante famille de paraboles
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MIRAGLIO, PIETRO. "ESTIMATES AND RIGIDITY FOR STABLE SOLUTIONS TO SOME NONLINEAR ELLIPTIC PROBLEMS." Doctoral thesis, Università degli Studi di Milano, 2020. http://hdl.handle.net/2434/704717.

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Questa tesi è incentrata sullo studio di equazioni differenziali alle derivate parziali di tipo ellittico. La prima parte della tesi riguarda la regolarità delle soluzioni stabili per un'equazione nonlineare con il p-Laplaciano, in un dominio limitato dello spazio Euclideo. La tecnica è basata sull'uso di disuguaglianze di tipo Hardy-Sobolev su ipersuperfici, del quale viene approfondito lo studio. Nella seconda parte viene preso in esame un problema nonlocale di tipo Dirichlet-Neumann. Studiamo la simmetria unidimensionale di alcune sottoclassi di soluzioni stabili, ottenendo risultati in dimensione n=2, 3. Inoltre, studiamo il comportamento asintotico dell'operatore associato a questo problema nonlocale, usando tecniche di Γ-convergenza.
This thesis deals with the study of elliptic PDEs. The first part of the thesis is focused on the regularity of stable solutions to a nonlinear equation involving the p-Laplacian, in a bounded domain of the Euclidean space. The technique is based on Hardy-Sobolev inequalities in hypersurfaces involving the mean curvature, which are also investigated in the thesis. The second part concerns, instead, a nonlocal problem of Dirichlet-to-Neumann type. We study the one-dimensional symmetry of some subclasses of stable solutions, obtaining new results in dimensions n=2, 3. In addition, we carry out the study of the asymptotic behaviour of the operator associated with this nonlocal problem, using Γ-convergence techniques.
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Marinov, Petko I. "Stability Analysis of Capillary Surfaces with Planar or Spherical Boundary in the Absence of Gravity." University of Toledo / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1290098654.

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Books on the topic "Mean curvature operator"

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Nonlinear elliptic equations of the second order. Providence, Rhode Island: American Mathematical Society, 2016.

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Li, Weiping, and Shihshu Walter Wei. Geometry and topology of submanifolds and currents: 2013 Midwest Geometry Conference, October 19, 2013, Oklahoma State University, Stillwater, Oklahoma : 2012 Midwest Geometry Conference, May 12-13, 2012, University of Oklahoma, Norman, Oklahoma. Providence, Rhode Island: American Mathematical Society, 2015.

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Book chapters on the topic "Mean curvature operator"

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Bertsch, Michiel, and Roberta Dal Passo. "A Parabolic Equation with a Mean-Curvature Type Operator." In Nonlinear Diffusion Equations and Their Equilibrium States, 3, 89–97. Boston, MA: Birkhäuser Boston, 1992. http://dx.doi.org/10.1007/978-1-4612-0393-3_6.

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Bereanu, Cristian, Petru Jebelean, and Jean Mawhin. "Multiple Radial Solutions at Resonance for Neumann Problems Involving the Mean Extrinsic Curvature Operator." In Analysis and Topology in Nonlinear Differential Equations, 87–101. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04214-5_5.

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Conference papers on the topic "Mean curvature operator"

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Bereanu, Cristian, Petru Jebelean, and Călin Şerban. "Dirichlet problems with mean curvature operator in Minkowski space." In 8th Congress of Romanian Mathematicians. WORLD SCIENTIFIC, 2016. http://dx.doi.org/10.1142/9789813142862_0001.

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Benevieri, Pierluigi, João Marcos do Ó, and Everaldo Souto de Medeiros. "Nonlinear systems with mean curvature-like operators." In Fixed Point Theory and its Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc77-0-3.

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Bereanu, Cristian, Petru Jebelean, Jean Mawhin, Alberto Cabada, Eduardo Liz, and Juan J. Nieto. "Radial solutions for systems involving mean curvature operators in Euclidean and Minkowski spaces." In MATHEMATICAL MODELS IN ENGINEERING, BIOLOGY AND MEDICINE: International Conference on Boundary Value Problems: Mathematical Models in Engineering, Biology and Medicine. AIP, 2009. http://dx.doi.org/10.1063/1.3142953.

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Torselletti, Enrico, Luigino Vitali, Erik Levold, and Kim J. Mo̸rk. "Submarine Pipeline Installation JIP: Strength and Deformation Capacity of Pipes Passing Over the S-Lay Vessel Stinger." In 25th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/omae2006-92378.

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The development of deep water gas fields using trunklines to carry the gas to the markets is sometime limited by the feasibility/economics of the construction phase. In particular there is a market for using S-lay vessels in water depth larger than 1000m. The S-lay feasibility depends on the applicable tension at the tensioner which is a function of water depth, stinger length and stinger curvature (for given stinger length by its curvature). This means that, without major vessel up-grading and to avoid too long stingers that are prone to damages caused by environmental loads, the application of larger stinger curvatures than presently allowed by current regulations/state of the art is needed. The work presented in this paper is a result of the project “Development of a Design Guideline for Submarine Pipeline Installation” sponsored by STATOIL and HYDRO. The technical activities are performed in co-operation by DNV, STATOIL and SNAMPROGETTI. The scope of the project is to produce a LRFD (Load Resistant Factor Design) design guideline to be used in the definition and application of design criteria for the laying phase e.g. to S and J-lay methods/equipment. The guideline covers D/t from 15 to 45 and applied strains over the overbend in excess of 0.5%. This paper addresses the failure modes relevant for combined high curvatures/strains, axial, external pressure and local forces due to roller over the stinger of an S-lay vessel and to sea bottom contacts, particularly: • Residual pipe ovality after laying, • Maximum strain and bending moment capacity. Analytical equations are proposed in accordance with DNV OS F101 philosophy and design format.
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Torselletti, Enrico, Luigino Vitali, Roberto Bruschi, Erik Levold, and Leif Collberg. "Submarine Pipeline Installation Joint Industry Project: Global Response Analysis of Pipelines During S-Laying." In 25th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/omae2006-92377.

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The development of deep water gas fields using trunklines to carry the gas to the markets is sometime limited by the feasibility/economics of the construction phase. In particular there is market for using S-lay vessel in water depth larger than 1000m. The S-lay feasibility depends on the applicable tension at the tensioner which is a function of water depth, stinger length and stinger curvature (for given stinger length by its curvature). This means that, without major vessel up-grading and to avoid too long stingers that are prone to damages caused by environmental loads, the application of larger stinger curvatures than allowed by current regulations/state of the art, is needed. The work presented in this paper is a result of the project “Development of a Design Guideline for Submarine Pipeline Installation” sponsored by STATOIL and HYDRO. The technical activities are performed in co-operation by DNV, STATOIL and SNAMPROGETTI. This paper presents the results of the analysed S-lay scenarios in relation to extended laying ability of medium to large diameter pipelines in order to define the statistical distribution of the relevant load effects, i.e. bending moment and longitudinal strain as per static/functional, dynamic/total, and environmental load effects. The results show that load effects (longitudinal applied strain and bending moment) are strongly influenced by the static setting (applied stinger curvature and axial force at the tensioner in combination with local roller reaction over the stinger). The load effect distributions are the basis for the development of design criteria/safety factors which fulfil a predefined target safety level.
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Ryan, Kevin J., Filippo Coletti, Christopher J. Elkins, and John K. Eaton. "Building Block Experiments in Discrete Hole Film Cooling." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-43731.

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This paper reports a series of building block experiments for discrete hole film cooling. Seven different configurations, including variations in injection wall curvature, mainstream pressure gradient, and boundary layer thickness are measured for a round film cooling hole, inclined 30 degrees at injection, and operated at a blowing ratio of unity. Full three dimensional, three component velocity fields and scalar coolant concentration fields are acquired using Magnetic Resonance Imaging (MRI) techniques. The results show the effect of varying the mainstream condition on the mean coolant concentration distribution and mean velocity field, including the counter-rotating vortex pair (CVP), a dominant feature of jet in crossflow type flows. The present study focuses on an analysis of the building block configurations only possible with full three dimensional velocity and concentration fields. Several scalar parameters including normalized perimeter, jet trajectory, maximum coolant concentration, and coolant concentration spread are extracted from the collected data and compared across the different configurations. The results indicate that the pressure gradient variations have the strongest effect on the calculated quantities, the boundary layer slightly less, and the curvature very little.
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7

Drabløs, Sigve Orheim, Katharina Haakenstad, Nils Sødahl, Kjell Herfjord, and Oddrun Steinkjer. "Global Dynamic Performance of Flexible Risers Employing Coupled Analysis." In ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/omae2015-41832.

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Flexible risers are inevitable in the operation of floating production units in intermediate water depths in harsh environments. The operation of flexible pipes under these conditions is challenging, and reliable and accurate analysis of the global performance of risers is vital. The main purpose of this paper is to describe an analysis method for the global performance of flexible risers taking advantages from advanced floater motion modelling and comprehensive modelling of the risers. The analysis scheme has been employed on a semi-submersible platform, operated in harsh environments in the North Sea and all its flexible risers and umbilicals have been analyzed. The platform motions are generated by means of a coupled vessel/slender structure model in which the vessel force model is introduced into a finite element model of the slender structures including the mooring lines and all its flexible risers. In this way all relevant coupling effects from damping, restoring and current loading on the slender structures are consistently included in the platform motion predictions. Subsequently each riser is analyzed in separate models with high element mesh resolution. The platform motions, in terms of low frequency and wave frequency motions obtained from the coupled model, are applied consistently with wave and current loading in the detailed riser model. In the detailed riser models, bending stiffeners are modelled with non-linear material behavior. The diffracted wave field is included in the wave loading of the risers. The stick-slip bending of the flexible pipes have been modelled for a selection of risers and the effect of this on the riser hang off loads and the curvature in the bend stiffener region is discussed. The main responses looked into have been the curvature in the bend stiffener region, the hang off loads and interference between risers and platform pontoons. The riser responses obtained from the coupled analysis scheme performed in the present work is compared to more standard analysis schemes where extreme offsets and transfer functions are used to generate platform motions.
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8

Bennett, H. E., and J. J. Shaffer. "Compact Optical Test Facility for Evaluating Very Long Focal Length Mirrors." In Optical Fabrication and Testing. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/oft.1980.ffa8.

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Various techniques have been used to test the optical figure and radius of curvature of optical flats and long focal length optics1. If optical flats become too large to be handled manually, they are often measured using a variant of the Ritchie-Common test, although Fizeau and Twyman-Green interferometers have also been used. The familiar knife-edge test is an excellent means for measuring the optical figure of a flat qualitatively using a well-corrected large parabola on an optical bench. It is also useful for measuring the figure and radius of curvature of concave spherical mirrors. If the radius of curvature is in the 10- to 100-m range, however, as is common for laser optics, air turbulence reduces the accuracy of the measurement. A more quantitative technique for recording the optical figure of long focal length optics and determining their radius of curvature is to use a "transmission sphere," basically a Fizeau interferometer modified for converging or diverging light. Parallel light incident on the transmission sphere is focussed by the lens, whose surface on the sample side is accurately normal to the exiting light beams. It thus is the reference surface in the modified Fizeau interferometer. Transmission spheres can be obtained in a variety of focal lengths and f numbers, but they are quite expensive and are specific for a relatively short range of f numbers in the mirrors tested. Air turbulence is a problem for long radius of curvature mirrors just as it is in the knife-edge test. The Zygo Corporation, which manufactures transmission spheres, also manufactures large beam expanders for testing optical flats of 30 cm (12 in.) in diameter or more. However, such large beam expanders are quite expensive. This paper describes a relatively inexpensive technique using the Zygo interferometer and one or more transmission spheres together with a large parabolic mirror or well-corrected lens and a fringe analysis system for testing both large optical flats and large, long focal length concave or convex mirrors. A range of focal lengths extending to infinity can be measured without utilizing long path lengths, thus minimizing air turbulence problems. Both concave and convex mirrors can be measured using the same transmission sphere, and unlike most other techniques for measuring long focal length optics, the longer the focal length the better the system operates.
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Haagensen, P. J., and T. I. Grøttum. "Fatigue Assessment of Drill Pipes." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-62696.

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Fatigue failures during offshore drilling operations is still a very costly problem. The fatigue behavior of drill pipes is reviewed, and typical failure modes are identified. The effects of drill string curvature during directional drilling on pipe body stress and on the fatigue life is examined. Effects on applied mean stress from drill string weight are discussed. Interaction effects of degradation mechanisms such as fatigue, wear and corrosion are evaluated. Experimental background data and statistical evaluation that form the basis for the current design practice issued by American Petroleum Institute (API) and other guidance in codes and standards is reviewed. Results from several recent testing programs performed under rotating bending of pipes with threaded connections, and tests involving the pipe body under resonance conditions are presented. The tests were made with pipe sizes from 2 7/8 in. to 5 7/8 in. in Grade S-135 pipes. The results are compared with published test data and design guidance such as API Recommended Practice G7 [1]. Recommendations are given for research and testing to improve reliability and the safe operation of drill strings.
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10

Kilner, Andrew, Ricardo Yoshioka, Hayden Marcollo, Rick Rogers, and Mohamed Taha. "Failure in Drilling Riser Auxiliary Line Attributed to VIV." In ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/omae2014-24681.

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Some drilling operators have experienced a loss of pressure from drilling riser auxiliary lines during operations. In some instances the loss of pressure has been as a result of auxiliary line seals experiencing excessive wear at the pin-box connection. In the case described within this paper, the failure was investigated and attributed to Vortex Induced Vibration of the main drilling riser. The rigid interface between the main riser and the outer auxiliary lines results in transfer of main drilling riser dynamic curvature motions directly into vertical axial motions at the pin-box connection. In the case considered, a high degree of VIV excitation was experienced through the drilling campaign which resulted in excessive wearing and ultimately failure of the pin-box seal. This paper presents a methodology to compute the auxiliary line axial displacement resulting from the drilling riser displacement and curvature. This methodology provides a means of estimating the relative axial motion of the pin-box connection when the main drilling riser is under VIV lock-in. It will also assist in identifying if excessive seal wear will be a concern during a drilling campaign. In this case it suggested that the limiting condition for the drilling riser was not fatigue of the main drilling riser, but wear of the pin-box seal. As a consequence of this investigation, it is recommended to include checks for excessive relative axial motion in general analysis methodology for deepwater drilling risers. As with VIV fatigue issues, the issue may be mitigated through VIV suppression.
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Reports on the topic "Mean curvature operator"

1

Fetcu, Dorel. Integral Submanifolds in Three-Sasakian Manifolds Whose Mean Curvature Vector Fields are Eigenvectors of the Laplace Operator. GIQ, 2012. http://dx.doi.org/10.7546/giq-9-2008-210-223.

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