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Journal articles on the topic 'Local curvature'

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Author: Grafiati

Published: 14 March 2023

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1

Milin Šipuš, Željka, and Blaženka Divjak. "Surfaces of Constant Curvature in the Pseudo-Galilean Space." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–28. http://dx.doi.org/10.1155/2012/375264.

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We develop the local theory of surfaces immersed in the pseudo-Galilean space, a special type of Cayley-Klein spaces. We define principal, Gaussian, and mean curvatures. By this, the general setting for study of surfaces of constant curvature in the pseudo-Galilean space is provided. We describe surfaces of revolution of constant curvature. We introduce special local coordinates for surfaces of constant curvature, so-called the Tchebyshev coordinates, and show that the angle between parametric curves satisfies the Klein-Gordon partial differential equation. We determine the Tchebyshev coordinates for surfaces of revolution and construct a surface with constant curvature from a particular solution of the Klein-Gordon equation.

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2

Zou, Weiyao, Kevin P. Thompson, and Jannick P. Rolland. "Differential Shack-Hartmann curvature sensor: local principal curvature measurements." Journal of the Optical Society of America A 25, no. 9 (August 21, 2008): 2331. http://dx.doi.org/10.1364/josaa.25.002331.

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3

Veronelli, Giona. "Scalar Curvature via Local Extent." Analysis and Geometry in Metric Spaces 6, no. 1 (November 1, 2018): 146–64. http://dx.doi.org/10.1515/agms-2018-0008.

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AbstractWe give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing the maximal distance between (n + 1) points in infinitesimally small neighborhoods of a point. Since this characterization is purely in terms of the distance function, it could be used to approach the problem of defining the scalar curvature on a non-smooth metric space. In the second part we will discuss this issue, focusing in particular on Alexandrov spaces and surfaces with bounded integral curvature.

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4

Garanzha, Vladimir A., Liudmila N. Kudryavtseva, and Dmitry A. Makarov. "Discrete curvatures for planar curves based on Archimedes’ duality principle." Russian Journal of Numerical Analysis and Mathematical Modelling 37, no. 2 (April 1, 2022): 85–98. http://dx.doi.org/10.1515/rnam-2022-0007.

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Abstract We introduce discrete curvatures for planar curves based on the construction of sequences of pairs of mutually dual polylines. For piecewise-regular curves consisting of a finite number of fragments of regular generalized spirals with definite (positive or negative) curvatures our discrete curvatures approximate the exact averaged curvature from below and from above. In order to derive these estimates one should provide a distance function allowing to compute the closest point on the curve for an arbitrary point on the plane.With refinement of the polylines, the averaged curvature over refined curve segments converges to the pointwise values of the curvature and, thus, we obtain a good and stable local approximation of the curvature. For the important engineering case when the curve is approximated only by the inscribed (primal) polyline and the exact distance function is not available, we provide a comparative analysis for several techniques allowing to build dual polylines and discrete curvatures and evaluate their ability to create lower and upper estimates for the averaged curvature.

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5

Huang, Y., and A. J. Rosakis. "Extension of Stoney’s Formula to Arbitrary Temperature Distributions in Thin Film/Substrate Systems." Journal of Applied Mechanics 74, no. 6 (February 9, 2006): 1225–33. http://dx.doi.org/10.1115/1.2744035.

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Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states that are assumed to remain uniform over the entire film/substrate system. By considering a circular thin film/substrate system subject to nonuniform and nonaxisymmetric temperature distributions, we derive relations between the film stresses and temperature, and between the plate system’s curvatures and the temperature. These relations featured a “local” part that involves a direct dependence of the stress or curvature components on the temperature at the same point, and a “nonlocal” part that reflects the effect of temperature of other points on the location of scrutiny. Most notably, we also derive relations between the polar components of the film stress and those of system curvatures which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary nonuniformities. These relations also feature a “nonlocal” dependence on curvatures making full-field measurements of curvature a necessity for the correct inference of stress. Finally, it is shown that the interfacial shear tractions between the film and the substrate are related to the gradients of the first curvature invariant and can also be inferred experimentally.

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6

SABOURAU, Stéphane. "Macroscopic scalar curvature and local collapsing." Annales scientifiques de l'École Normale Supérieure 55, no. 4 (July 2022): 919–36. http://dx.doi.org/10.24033/asens.2509.

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7

Nietiadi, Maureen L., and Herbert M. Urbassek. "Influence of local curvature on sputtering." Applied Physics Letters 103, no. 11 (September 9, 2013): 113108. http://dx.doi.org/10.1063/1.4821294.

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8

Rueda, Sylvia, Jayaram K. Udupa, and Li Bai. "Shape modeling via local curvature scale." Pattern Recognition Letters 31, no. 4 (March 2010): 324–36. http://dx.doi.org/10.1016/j.patrec.2009.09.007.

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9

Helliwell, T. M., and D. A. Konkowski. "Cosmic strings: Gravitation without local curvature." American Journal of Physics 55, no. 5 (May 1987): 401–7. http://dx.doi.org/10.1119/1.15145.

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10

Li, H., and S. Q. Liu. "Local interpolation of curvature-continuous surfaces." Computer-Aided Design 24, no. 9 (September 1992): 491–503. http://dx.doi.org/10.1016/0010-4485(92)90029-a.

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11

Ferrie, F. P., and J. Lagarde. "Curvature consistency improves local shading analysis." CVGIP: Image Understanding 55, no. 1 (January 1992): 95–105. http://dx.doi.org/10.1016/1049-9660(92)90009-r.

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12

Chang, Dongfeng, and Apostolos Serletis. "Imposing local curvature in the QUAIDS." Economics Letters 115, no. 1 (April 2012): 41–43. http://dx.doi.org/10.1016/j.econlet.2011.11.033.

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13

Jost, Jürgen, and Shiping Liu. "Ollivier’s Ricci Curvature, Local Clustering and Curvature-Dimension Inequalities on Graphs." Discrete & Computational Geometry 51, no. 2 (November 13, 2013): 300–322. http://dx.doi.org/10.1007/s00454-013-9558-1.

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14

Vaccaro, Marzia Sara, Francesco Marotti de Sciarra, and Raffaele Barretta. "On the regularity of curvature fields in stress-driven nonlocal elastic beams." Acta Mechanica 232, no. 7 (April 26, 2021): 2595–603. http://dx.doi.org/10.1007/s00707-021-02967-w.

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AbstractElastostatic problems of Bernoulli–Euler nanobeams, involving internal kinematic constraints and discontinuous and/or concentrated force systems, are investigated by the stress-driven nonlocal elasticity model. The field of elastic curvature is output by the convolution integral with a special averaging kernel and a piecewise smooth source field of elastic curvature, pointwise generated by the bending interaction. The total curvature is got by adding nonelastic curvatures due to thermal and/or electromagnetic effects and similar ones. It is shown that fields of elastic curvature, associated with piecewise smooth source fields and bi-exponential kernel, are continuously differentiable in the whole domain. The nonlocal elastic stress-driven integral law is then equivalent to a constitutive differential problem equipped with boundary and interface constitutive conditions expressing continuity of elastic curvature and its derivative. Effectiveness of the interface conditions is evidenced by the solution of an exemplar assemblage of beams subjected to discontinuous and concentrated loadings and to thermal curvatures, nonlocally associated with discontinuous thermal gradients. Analytical solutions of structural problems and their nonlocal-to-local limits are evaluated and commented upon.

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15

Guilfoyle, Brendan S. "The local moduli of Sasakian3-manifolds." International Journal of Mathematics and Mathematical Sciences 32, no. 2 (2002): 117–27. http://dx.doi.org/10.1155/s0161171202006774.

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The Newman-Penrose-Perjes formalism is applied to Sasakian3-manifolds and the local form of the metric and contact structure is presented. The local moduli space can be parameterised by a single function of two variables and it is shown that, given any smooth function of two variables, there exists locally a Sasakian structure with scalar curvature equal to this function. The case where the scalar curvature is constant(η-Einstein Sasakian metrics) is completely solved locally. The resulting Sasakian manifolds includeS 3,Nil, andSL˜ 2 (ℝ), as well as the Berger spheres. It is also shown that a conformally flat Sasakian3-manifold is Einstein of positive scalar curvature.

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16

Xu, Y. F., and J. S. Kim. "Baseline-Free Structural Damage Identification for Beam-Like Structures Using Curvature Waveforms of Propagating Flexural Waves." Sensors 21, no. 7 (April 2, 2021): 2453. http://dx.doi.org/10.3390/s21072453.

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Curvatures in mode shapes and operating deflection shapes have been extensively studied for vibration-based structural damage identification in recent decades. Curvatures of mode shapes and operating deflection shapes have proved capable of localizing and manifesting local effects of damage on mode shapes and operating deflection shapes in forms of local anomalies. The damage can be inversely identified in the neighborhoods of the anomalies that exist in the curvatures. Meanwhile, propagating flexural waves have also been extensively studied for structural damage identification and proved to be effective, thanks to their high damage-sensitivity and long range of propagation. In this work, a baseline-free structural damage identification method is developed for beam-like structures using curvature waveforms of propagating flexural waves. A multi-resolution local-regression temporal-spatial curvature damage index (TSCDI) is defined in a pointwise manner. A two-dimensional auxiliary TSCDI and a one-dimensional auxiliary damage index are developed to further assist the identification. Two major advantages of the proposed method are: (1) curvature waveforms of propagating flexural waves have relatively high signal-to-noise ratios due to the use of a multi-resolution central finite difference scheme, so that the local effects of the damage can be manifested, and (2) the proposed method does not require quantitative knowledge of a pristine structure associated with a structure to be examined, such as its material properties, waveforms of propagating flexural waves and boundary conditions. Numerical and experimental investigations of the proposed method are conducted on damaged beam-like structures, and the effectiveness of the proposed method is verified by the results of the investigations.

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17

Tamaki, Teruyuki, Kenichi Murakami, Hotaka Homma, and Kohsaku Ushioda. "Two-Dimensional Grain Growth Simulation by Local Curvature Multi-Vertex Model." Materials Science Forum 715-716 (April 2012): 551–56. http://dx.doi.org/10.4028/www.scientific.net/msf.715-716.551.

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A local curvature multi-vertex model was developed. This model is the straightforward two-dimensional topological network model based on the physical principles which are the curvatures of grain boundaries and the grain boundary tensions at triple junctions. The model was applied to the artificial random microstructure under some conditions of grain boundary characters. The misorientation distribution was changed very little under constant grain boundary energy and mobility, but it was change much under grain boundary character dependent on misorientation. Therefore, in order to discuss actual textures, it is important to take grain boundary characters into account.

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18

Lee, Jung-Ho, Wan-Sok Choi, and Jong-Whan Jang. "An Improved Snake Algorithm Using Local Curvature." KIPS Transactions:PartB 15B, no. 6 (December 31, 2008): 501–6. http://dx.doi.org/10.3745/kipstb.2008.15-b.6.501.

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19

Prüfer, Friedbert, Franco Tricerri, and Lieven Vanhecke. "Curvature invariants, differential operators and local homogeneity." Transactions of the American Mathematical Society 348, no. 11 (1996): 4643–52. http://dx.doi.org/10.1090/s0002-9947-96-01686-8.

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20

Wijntjes, M. W. A., A. Sato, V. Hayward, and A. M. L. Kappers. "Local Surface Orientation Dominates Haptic Curvature Discrimination." IEEE Transactions on Haptics 2, no. 2 (April 2009): 94–102. http://dx.doi.org/10.1109/toh.2009.1.

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21

Wise, Daniel T. "Sectional curvature, compact cores, and local quasiconvexity." Geometric And Functional Analysis 14, no. 2 (April 1, 2004): 433–68. http://dx.doi.org/10.1007/s00039-004-0463-x.

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22

Lu, Peng. "A local curvature bound in Ricci flow." Geometry & Topology 14, no. 2 (April 10, 2010): 1095–110. http://dx.doi.org/10.2140/gt.2010.14.1095.

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23

Tang, Yunqing. "Algebraic solutions of differential equations over ℙ1 −{0,1,∞}." International Journal of Number Theory 14, no. 05 (May 28, 2018): 1427–57. http://dx.doi.org/10.1142/s1793042118500884.

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The Grothendieck–Katz [Formula: see text]-curvature conjecture predicts that an arithmetic differential equation whose reduction modulo [Formula: see text] has vanishing [Formula: see text]-curvatures for almost all [Formula: see text] has finite monodromy. It is known that it suffices to prove the conjecture for differential equations on [Formula: see text] We prove a variant of this conjecture for [Formula: see text] which asserts that if the equation satisfies a certain convergence condition for all [Formula: see text] then its monodromy is trivial. For those [Formula: see text] for which the [Formula: see text]-curvature makes sense, its vanishing implies our condition. We deduce from this a description of the differential Galois group of the equation in terms of [Formula: see text]-curvatures and certain local monodromy groups. We also prove similar variants of the [Formula: see text]-curvature conjecture for an elliptic curve with [Formula: see text]-invariant [Formula: see text] minus its identity and for [Formula: see text].

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24

Lipnickas, Arūnas, and Vidas Raudonis. "Contour Representation by Clustering Curvatures of the 3D Objects." Solid State Phenomena 147-149 (January 2009): 633–38. http://dx.doi.org/10.4028/www.scientific.net/ssp.147-149.633.

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The purpose of this work is to segment large size triangulated surfaces and the contours extraction of the 3D object by the use of the object curvature value. The curvatures values allow categorizing the type of the local surface of the 3D object. In present work the curvature was estimated for the free-form surfaces obtained by the 3D range scanner. A free-form surface is the surface such that the surface normal is defined and continuous everywhere, except at sharp corners and edges [2, 5]. Two types of distance measurements functions based on Euclidian distance, bounded box and topology of surface were used for the curvature estimation. Clustering technique has been involved to cluster the values of the curvature for 3D object contour representation. The described technique was applied to the 3D objects with free-form surfaces such as the human foot and cube.

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25

Benedini Riul, P., and R. Oset Sinha. "A relation between the curvature ellipse and the curvature parabola." Advances in Geometry 19, no. 3 (July 26, 2019): 389–99. http://dx.doi.org/10.1515/advgeom-2019-0002.

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Abstract At each point in an immersed surface in ℝ4 there is a curvature ellipse in the normal plane which codifies all the local second order geometry of the surface. Recently, at the singular point of a corank 1 singular surface in ℝ3, a curvature parabola in the normal plane which codifies all the local second order geometry has been defined. When projecting a regular surface in ℝ4 to ℝ3 in a tangent direction, corank 1 singularities appear generically. The projection has a cross-cap singularity unless the direction of projection is asymptotic, where more degenerate singularities can appear. In this paper we relate the geometry of an immersed surface in ℝ4 at a certain point to the geometry of the projection of the surface to ℝ3 at the singular point. In particular we relate the curvature ellipse of the surface to the curvature parabola of its singular projection.

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26

Zhang, Fan, Bao Sheng Kang, and Jian Dong Zhao. "Robust Curvature Estimation on Scattered Point Cloud." Applied Mechanics and Materials 303-306 (February 2013): 2198–202. http://dx.doi.org/10.4028/www.scientific.net/amm.303-306.2198.

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A robust statistics approach to curvature estimation on scattered point cloud is presented. The basic idea of this method is fitting a surface to the local shape at a sample point in 3D and the curvatures are computed for this fitted surface. Within a Maximum Kernel Density Estimator framework, the best fitted surface for each point is obtained. Therefore the algorithm is robust with respect to noise and outliers. Experiments show that our method has achieved satisfactory results.

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27

Bruce, J. W., and F. Tari. "Extrema of principal curvature and symmetry." Proceedings of the Edinburgh Mathematical Society 39, no. 2 (June 1996): 397–402. http://dx.doi.org/10.1017/s0013091500023129.

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In this paper we show that away from umbilic points certain measures of the local reflectional symmetry of a surface in Euclidean 3-space are detected by the extrema of the sectional curvatures along lines of curvature. There are two types of reflectional symmetry, with one detected by the contact between the surface and spheres, and in this case the result is due to Porteous and is 20 years old. We show that an analogous result remains true for the second type of symmetry.

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28

SAZDOVIĆ, B. "CT-DUALITY AS A LOCAL PROPERTY OF THE WORLDSHEET." Modern Physics Letters A 20, no. 12 (April 20, 2005): 897–910. http://dx.doi.org/10.1142/s0217732305017160.

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In this present article, we study the local features of the worldsheet in the case when probe bosonic string moves in antisymmetric background field. We generalize the geometry of surfaces embedded in spacetime to the case when the torsion is present. We define the mean extrinsic curvature for spaces with Minkowski signature and introduce the concept of mean torsion. Its orthogonal projection defines the dual mean extrinsic curvature. In this language, the field equation is just the equality of mean extrinsic curvature and extrinsic mean torsion, which we call CT-duality. To the worldsheet described by this relation we will refer as CT-dual surface.

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29

CAPOZZIELLO, S., and M. DE LAURENTIS. "GRAVITY FROM LOCAL POINCARÉ GAUGE INVARIANCE." International Journal of Geometric Methods in Modern Physics 06, no. 01 (February 2009): 1–24. http://dx.doi.org/10.1142/s0219887809003400.

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A compact, self-contained approach to gravitation, based on the local Poincaré gauge invariance, is proposed. Starting from the general invariance principle, we discuss the global and the local Poincaré invariance developing the spinor, vector and tetrad formalisms. These tools allow to construct the curvature, torsion and metric tensors by the Fock–Ivanenko covariant derivative. The resulting Einstein–Cartan theory describes a space endowed with non-vanishing curvature and torsion while the gravitational field equations are similar to the Yang–Mills equations of motion with the torsion tensor playing the role of the Yang–Mills field strength.

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30

Schulze, Felix, and Brian White. "A local regularity theorem for mean curvature flow with triple edges." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 758 (January 1, 2020): 281–305. http://dx.doi.org/10.1515/crelle-2017-0044.

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AbstractMean curvature flow of clusters of n-dimensional surfaces in {\mathbb{R}^{n+k}} that meet in triples at equal angles along smooth edges and higher order junctions on lower-dimensional faces is a natural extension of classical mean curvature flow. We call such a flow a mean curvature flow with triple edges. We show that if a smooth mean curvature flow with triple edges is weakly close to a static union of three n-dimensional unit density half-planes, then it is smoothly close. Extending the regularity result to a class of integral Brakke flows, we show that this implies smooth short-time existence of the flow starting from an initial surface cluster that has triple edges, but no higher order junctions.

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31

Massamba, Fortuné, and Samuel Ssekajja. "A geometric flow on null hypersurfaces of Lorentzian manifolds." Topological Algebra and its Applications 10, no. 1 (January 1, 2022): 185–95. http://dx.doi.org/10.1515/taa-2022-0126.

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Abstract We introduce a geometric flow on a screen integrable null hypersurface in terms of its local second fundamental form. We use it to give an alternative proof to the vorticity free Raychaudhuri’s equation for null hypersurface, as well as establishing conditions for the existence of constant mean curvature (CMC) null hypersurfaces, and leaves of constant scalar curvatures.

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32

LIDSEY, JAMES E. "NON-LOCAL INFLATION AROUND A LOCAL MAXIMUM." International Journal of Modern Physics D 17, no. 03n04 (March 2008): 577–82. http://dx.doi.org/10.1142/s0218271808012292.

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It is shown that non-local, higher-derivative operators, which arise generically in string field theory, can act as additional sources of friction on the inflaton field as it rolls away from a maximum in its potential. Moreover, the cosmic dynamics can be quantified in terms of a local field theory, where the curvature of an effective potential has been suppressed. A prolonged phase of quasi-exponential expansion can therefore be realised with steep potentials that typically arise in particle physics models. We illustrate this effect within the context of p-adic string theory.

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33

Kang, Donghoon, and Wonseok Chung. "Estimation of Curvature Changes for Steel-Concrete Composite Bridge Using Fiber Bragg Grating Sensors." Advances in Materials Science and Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/405143.

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This study is focused on the verification of the key idea of a newly developed steel-concrete composite bridge. The key idea of the proposed bridge is to reduce the design moment by applying vertical prestressing force to steel girders, so that a moment distribution of a continuous span bridge is formed in a simple span bridge. For the verification of the key technology, curvature changes of the bridge should be monitored sequentially at every construction stage. A pair of multiplexed FBG sensor arrays is proposed in order to measure curvature changes in this study. They are embedded in a full-scale test bridge and measured local strains, which are finally converted to curvatures. From the result of curvature changes, it is successfully ensured that the key idea of the proposed bridge, expected theoretically, is viable.

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34

Blumentritt, Charles H., Kurt J. Marfurt, and E. Charlotte Sullivan. "Volume-based curvature computations illuminate fracture orientations — Early to mid-Paleozoic, Central Basin Platform, west Texas." GEOPHYSICS 71, no. 5 (September 2006): B159—B166. http://dx.doi.org/10.1190/1.2335581.

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Volumetric curvature analysis is a simple but computationally intensive procedure that provides insight into fracture orientation and regional stresses. Until recently, curvature analysis has been limited to computation along horizon surfaces that may be affected by unintentional bias and picking errors introduced during the interpretation process. Volumetric curvature is best estimated in a two-step process. In the first step, we use a moving-analysis subvolume to estimate volumetric reflector dip and azimuth for the best-fit tangent plane for each sample in the full volume. In the second step, we calculate curvature from adjacent measures of dip and azimuth. We use larger curvature analysis windows to estimate longer wavelength curvatures. Such a technique allows us to output full 3D volumes of curvature values for one or more scales of analysis. We apply these techniques to a data set from the Central Basin Platform of west Texas and find lineaments not observable with other seismic attributes. These lineaments indicate that, in the lower Paleozoic interval, a left-lateral shear couple oriented due east-west controls the local stress regime. Such a model predicts that extension faulting and fractures will be oriented northeast-southwest. The example demonstrates the potential of this new technology to determine stress regimes and predict azimuths of open fractures.

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35

Li, Yi, and Yuan Yuan. "Local curvature estimates along the κ-LYZ flow." Journal of Geometry and Physics 164 (June 2021): 104162. http://dx.doi.org/10.1016/j.geomphys.2021.104162.

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36

Ecker, Klaus. "A Local Monotonicity Formula for Mean Curvature Flow." Annals of Mathematics 154, no. 2 (September 2001): 503. http://dx.doi.org/10.2307/3062105.

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37

Li, Yi. "Local curvature estimates for the Ricci-harmonic flow." Nonlinear Analysis 222 (September 2022): 112961. http://dx.doi.org/10.1016/j.na.2022.112961.

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38

DE, UDAY CHAND, and SAMEH SHENAWY. "ON LOCAL CURVATURE SYMMETRIES OF GRW SPACE-TIMES." Reports on Mathematical Physics 88, no. 3 (December 2021): 313–25. http://dx.doi.org/10.1016/s0034-4877(21)00083-5.

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39

Kluge, Christoph, Matthias Pöhnl, and Rainer A. Böckmann. "Spontaneous local membrane curvature induced by transmembrane proteins." Biophysical Journal 121, no. 5 (March 2022): 671–83. http://dx.doi.org/10.1016/j.bpj.2022.01.029.

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40

Acunzo, Adriano, Francesco Bajardi, and Salvatore Capozziello. "Non-local curvature gravity cosmology via Noether symmetries." Physics Letters B 826 (March 2022): 136907. http://dx.doi.org/10.1016/j.physletb.2022.136907.

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41

White, Brian. "A local regularity theorem for mean curvature flow." Annals of Mathematics 161, no. 3 (May 1, 2005): 1487–519. http://dx.doi.org/10.4007/annals.2005.161.1487.

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42

Moschini, Giancarlo. "Imposing Local Curvature Conditions in Flexible Demand Systems." Journal of Business & Economic Statistics 17, no. 4 (October 1999): 487. http://dx.doi.org/10.2307/1392406.

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43

Shawcroft, Paul. "Detecting negative curvature in groups via local conditions." Proceedings of the American Mathematical Society 122, no. 4 (April 1, 1994): 1015. http://dx.doi.org/10.1090/s0002-9939-1994-1249891-2.

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44

Moschini, Giancarlo. "Imposing Local Curvature Conditions in Flexible Demand Systems." Journal of Business & Economic Statistics 17, no. 4 (October 1999): 487–90. http://dx.doi.org/10.1080/07350015.1999.10524837.

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45

Poon, W. Y., and Y. S. Poon. "Conformal normal curvature and assessment of local influence." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 61, no. 1 (February 1999): 51–61. http://dx.doi.org/10.1111/1467-9868.00162.

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46

Druet, Olivier. "Sharp local isoperimetric inequalities involving the scalar curvature." Proceedings of the American Mathematical Society 130, no. 8 (March 12, 2002): 2351–61. http://dx.doi.org/10.1090/s0002-9939-02-06355-4.

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47

Schroeder, Viktor, and Martin Strake. "Local rigidity of symmetric spaces of nonpositive curvature." Proceedings of the American Mathematical Society 106, no. 2 (February 1, 1989): 481. http://dx.doi.org/10.1090/s0002-9939-1989-0929404-0.

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48

Humpert, Christof, and Martin Baumann. "Local membrane curvature affects spontaneous membrane fluctuation characteristics." Molecular Membrane Biology 20, no. 2 (January 2003): 155–62. http://dx.doi.org/10.1080/09687680307080.

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Zhao, Qing, Efthymios I. Ioannidis, and Heather J. Kulik. "Global and local curvature in density functional theory." Journal of Chemical Physics 145, no. 5 (August 7, 2016): 054109. http://dx.doi.org/10.1063/1.4959882.

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HENKEL, OLIVER. "Local prescribed mean curvature foliations in cosmological spacetimes." Mathematical Proceedings of the Cambridge Philosophical Society 134, no. 3 (May 2003): 551–71. http://dx.doi.org/10.1017/s0305004102006515.

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