Relevant bibliographies by topics / Minimal Lagrangian Submanifolds

Academic literature on the topic 'Minimal Lagrangian Submanifolds'

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Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Minimal Lagrangian Submanifolds"

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Iriyeh, Hiroshi. "Symplectic topology of Lagrangian submanifolds of ℂPn with intermediate minimal Maslov numbers." Advances in Geometry 17, no. 2 (March 28, 2017): 247–64. http://dx.doi.org/10.1515/advgeom-2017-0005.

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AbstractWe examine symplectic topological features of a certain family of monotone Lagrangian submanifolds in ℂPn. First we give cohomological constraints on a Lagrangian submanifold in ℂPn whose first integral homology is p-torsion. In the case where (n, p) = (5,3), (8, 3), we prove that the cohomologies with coefficients in ℤ2 of such Lagrangian submanifolds are isomorphic to that of SU(3)/(SO(3)ℤ3) and SU(3)/ℤ3, respectively. Then we calculate the Floer cohomology with coefficients in ℤ2 of a monotone Lagrangian submanifold SU(p)/ℤp in ${\mathbb C}P^{p^2-1}.$
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Bolton, J., C. Rodriguez Montealegre, and L. Vrancken. "Characterizing warped-product Lagrangian immersions in complex projective space." Proceedings of the Edinburgh Mathematical Society 52, no. 2 (May 28, 2009): 273–86. http://dx.doi.org/10.1017/s0013091507000922.

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AbstractStarting from two Lagrangian immersions and a horizontal curve in S3(1), it is possible to construct a new Lagrangian immersion, which we call a warped-product Lagrangian immersion. In this paper, we find two characterizations of warped-product Lagrangian immersions. We also investigate Lagrangian submanifolds which attain at every point equality in the improved version of Chen's inequality for Lagrangian submanifolds of ℂPn(4) as discovered by Opreaffi We show that, for n≥4, an n-dimensional Lagrangian submanifold in ℂPn(4) for which equality is attained at all points is necessarily minimal.
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Blair, David E. "On Lagrangian Catenoids." Canadian Mathematical Bulletin 50, no. 3 (September 1, 2007): 321–33. http://dx.doi.org/10.4153/cmb-2007-031-4.

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AbstractRecently I. Castro and F.Urbano introduced the Lagrangian catenoid. Topologically, it is ℝ × Sn–1 and its induced metric is conformally flat, but not cylindrical. Their result is that if a Lagrangian minimal submanifold in ℂn is foliated by round (n – 1)-spheres, it is congruent to a Lagrangian catenoid. Here we study the question of conformally flat, minimal, Lagrangian submanifolds in ℂn. The general problem is formidable, but we first show that such a submanifold resembles a Lagrangian catenoid in that its Schouten tensor has an eigenvalue of multiplicity one. Then, restricting to the case of at most two eigenvalues, we show that the submanifold is either flat and totally geodesic or is homothetic to (a piece of) the Lagrangian catenoid.
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Ohnita, Yoshihiro. "Minimal Maslov number of R-spaces canonically embedded in Einstein-Kähler C-spaces." Complex Manifolds 6, no. 1 (January 1, 2019): 303–19. http://dx.doi.org/10.1515/coma-2019-0016.

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AbstractAn R-space is a compact homogeneous space obtained as an orbit of the isotropy representation of a Riemannian symmetric space. It is known that each R-space has the canonical embedding into a Kähler C-space as a real form, and thus a compact embedded totally geodesic Lagrangian submanifold. The minimal Maslov number of Lagrangian submanifolds in symplectic manifolds is one of invariants under Hamiltonian isotopies and very fundamental to study the Floer homology for intersections of Lagrangian submanifolds. In this paper we show a Lie theoretic formula for the minimal Maslov number of R-spaces canonically embedded in Einstein-Kähler C-spaces, and provide some examples of the calculation by the formula.
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Tevdoradze, Z. "The Hörmander and Maslov Classes and Fomenko's Conjecture." gmj 4, no. 2 (April 1997): 185–200. http://dx.doi.org/10.1515/gmj.1997.185.

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Abstract Some functorial properties are studied for the Hörmander classes defined for symplectic bundles. The behavior of the Chern first form on a Lagrangian submanifold in an almost Hermitian manifold is also studied, and Fomenko's conjecture about the behavior of a Maslov class on minimal Lagrangian submanifolds is considered.
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CHEN, BANG-YEN. "Ideal Lagrangian immersions in complex space forms." Mathematical Proceedings of the Cambridge Philosophical Society 128, no. 3 (May 2000): 511–33. http://dx.doi.org/10.1017/s0305004199004247.

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Roughly speaking, an ideal immersion of a Riemannian manifold into a space form is an isometric immersion which produces the least possible amount of tension from the ambient space at each point of the submanifold. In this paper we study Lagrangian immersions in complex space forms which are ideal. We prove that all Lagrangian ideal immersions in a complex space form are minimal. We also determine ideal Lagrangian submanifolds in complex space forms.
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Bektaş, Burcu, Marilena Moruz, Joeri Van der Veken, and Luc Vrancken. "Lagrangian submanifolds of the nearly Kähler 𝕊3 × 𝕊3 from minimal surfaces in 𝕊3." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 03 (December 27, 2018): 655–89. http://dx.doi.org/10.1017/prm.2018.43.

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AbstractWe study non-totally geodesic Lagrangian submanifolds of the nearly Kähler 𝕊3 × 𝕊3 for which the projection on the first component is nowhere of maximal rank. We show that this property can be expressed in terms of the so-called angle functions and that such Lagrangian submanifolds are closely related to minimal surfaces in 𝕊3. Indeed, starting from an arbitrary minimal surface, we can construct locally a large family of such Lagrangian immersions, including one exceptional example. We also show that locally all such Lagrangian submanifolds can be obtained in this way.
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Butscher, Adrian. "Deformations of minimal Lagrangian submanifolds with boundary." Proceedings of the American Mathematical Society 131, no. 6 (October 24, 2002): 1953–64. http://dx.doi.org/10.1090/s0002-9939-02-06800-4.

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Mironov, Andrei E., and Taras E. Panov. "Hamiltonian-minimal Lagrangian submanifolds in toric varieties." Russian Mathematical Surveys 68, no. 2 (April 30, 2013): 392–94. http://dx.doi.org/10.1070/rm2013v068n02abeh004835.

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Maccheroni, Roberta. "Complex analytic properties of minimal Lagrangian submanifolds." Journal of Symplectic Geometry 18, no. 4 (2020): 1127–46. http://dx.doi.org/10.4310/jsg.2020.v18.n4.a6.

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Dissertations / Theses on the topic "Minimal Lagrangian Submanifolds"

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Goldstein, Edward 1977. "Calibrations and minimal Lagrangian submanifolds." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/8639.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.
Includes bibliographical references (p. 119-122).
This thesis will be concerned with the geometry of minimal submanifolds in certain Riemannian manifolds which possess some special geometric structure. Those Riemannian manifolds will fall into one of the following categories: 1) A Riemannian manifold M with a calibrating k-form n7. We will derive some intrinsic volume comparison results for calibrated submanifolds of M and give some basic applications to their intrinsic geometry. 2) A Kahler n-fold M with a nowhere vanishing holomorphic (n, 0)-form (we will call'M an almost Calabi-Yau manifold). We will study the geometry of Special Lagrangian submanifolds on M and the global properties of their moduli-space. We will exhibit an example of a compact, simply connected almost Calabi-Yau threefold, which admits a Special Lagrangian torus fibration. We will also show how to construct Special Lagrangian fibrations on non-compact almost Calabi-Yau manifolds using torus actions and give numerous examples of such fibrations. 3) A Kahler-Einstein manifold M with non-zero scalar curvature. We will study the geometry of minimal Lagrangian submanifolds in M and their interaction with the geometry of M. We will also construct some new families of minimal Lagrangian submanifolds in toric Kahler-Einstein manifolds. 4) A Riemannian 7-manifold with holonomy G2. We will construct some new examples of coassociative submanifolds on complete Riemannian 7-manifolds with holonomy G2 via group actions.
by Edward Goldstein.
Ph.D.
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ROSSI, FEDERICO ALBERTO. "D-Complex Structures on Manifolds: Cohomological properties and deformations." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2013. http://hdl.handle.net/10281/41976.

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In questa tesi studiamo alcune proprietà delle "Varietà Doppie" o D-Varietà. In particolare studiamo la teoria delle deformazioni di D-Strutture e di D-Strutture CR, e troviamo una condizione che è equivalente alla classica condizione di Maurer-Cartan che descrive l'integrabilità di deformazioni di D-Strutture. Successivamente prestiamo attenzione alla coomologia delle D-Varietà, provando che una versione D-complessa del del-delbar-Lemma non può essere vera per D-varietà compatte. Inoltre sono stabilite alcune proprietà di sottogruppi speciali della coomologia di de-Rham, ottenute studiando il loro comportamento sotto l'azione di deformazioni. Infine, un risultato riguardante le sottovarietà Lagrangiane minimali dovuto ad Harvey e Lawson riguardante le varietà D-Kahler Ricci-Piatte è generalizzato a una classe di varietà simplettiche quasi D-complesse.
We study some properties of Double Manifold, or D-Manifolds. In particular, we study of deformations of D-structures and of CR D-structures, and we found a condition which is equivalent to the classical Maurer-Cartan equation describing the integrability of the deformations. We also focus on the cohomological properties of D-Manifold, showing that a del-delbar-Lemma can not hold for any compact D-Manifold. We also state some properties of special subgroups of de-Rham cohomology, studing also their behaviour under small deformations. Finally, a result by Harvey and Lawson about the minimal Lagrangian Submanifold of a D-Kahler Ricci-flat manifold is generalized to the case of a special almost D-complex symplectic manifold.
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Su, Wei-Bo, and 蘇瑋栢. "Stability of Minimal Lagrangian Submanifolds and Soliton Solutions for Lagrangian Mean Curvature Flow." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/5ae889.

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博士
國立臺灣大學
數學研究所
107
Stability provides important information about critical points of some functionals. In this thesis, the class of functionals we are interested in are the $f$-volume functionals defined on the space of Lagrangian submanifolds in a K"ahler manifold $X$, where $f$ is a function on $X$. The critical points for the $f$-volume functional are called the $f$-minimal Lagrangian submanifolds, which are generalizations of minimal Lagrangian submanifolds and soliton solutions for Lagrangian mean curvature flow. We study two different notions of stability with respect to the $f$-volume functional, namely the linear stability and dynamic stability. The linear stability concerning the positivity of second variation of $f$-volume functional at an $f$-minimal Lagrangian submanifold. We derive a second variation formula for $f$-minimal Lagrangian submanifolds, which is a generalization of the second variation formula by Chen [Che81] and Oh [Oh90]. Using this we obtain stability criterions for $f$-minimal Lagrangian submanifolds in gradient K"ahler--Ricci solitons. In particular, we show that expanding and translating solitons for Lagrangian mean curvature flow are $f$-stable. The dynamic stability on the other hand regarding the existence and convergence of the negative gradient flow of the $f$-volume functional, the generalized Lagrangian mean curvature flow, starting from an initial data nearby a critical point. Since the examples of $f$-minimal Lagrangians we are most interested in are complete noncompact, we first prove a short-time existence for asymptotically conical Lagrangian mean curvature flow. Then we give some long-time existence and convergence results for equivariant, almost-calibrated, asymptotically conical Lagrangian mean curvature flow in $mathbb{C}^{m}$.
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Books on the topic "Minimal Lagrangian Submanifolds"

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Mann, Peter. Constrained Lagrangian Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0008.

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This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations using Lagrange multipliers; these can be used to reduce the number of coordinates until a linearly independent minimal set is obtained that describes a constraint surface within configuration space, so that Lagrange equations can be set up and solved. Motion is understood to be confined to a constraint submanifold. The variational formulation of non-holonomic constraints is then discussed to derive the vakonomic formulation. These erroneous equations are then compared to the central Lagrange equation, and the precise nature of the variations used in each formulation is investigated. The vakonomic equations are then presented in their Suslov form (Suslov–vakonomic form) in an attempt to reconcile the two approaches. In addition, the structure of biological membranes is framed as a constrained optimisation problem.
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Book chapters on the topic "Minimal Lagrangian Submanifolds"

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Bryant, Robert L. "Minimal lagrangian submanifolds of Kähler-einstein manifolds." In Lecture Notes in Mathematics, 1–12. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0077676.

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Miyaoka, Reiko, and Satoshi Ueki. "Stability of Complete Minimal Lagrangian Submanifold and L 2 Harmonic 1-Forms." In Springer Proceedings in Mathematics & Statistics, 89–95. Tokyo: Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-55215-4_8.

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"Complex and Lagrangian submanifolds in pseudo-Kähler manifolds." In Minimal Submanifolds in Pseudo-Riemannian Geometry, 111–50. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814291255_0005.

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Conference papers on the topic "Minimal Lagrangian Submanifolds"

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EJIRI, N. "COMPLEX SUBMANIFOLDS AND LAGRANGIAN SUBMANIFOLDS ASSOCIATE WITH MINIMAL SURFACES IN TORI." In Proceedings of the 8th International Workshop on Complex Structures and Vector Fields. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812709806_0009.

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