Results 1 to 10 of about 1,076 (51)
Widths of balls and free boundary minimal submanifolds
Advanced Nonlinear Studies, 2023 We observe that the kk-dimensional width of an nn-ball in a space form is given by the area of an equatorial kk-ball. We also discuss the relationship between widths and lower bounds for the area of a free boundary minimal submanifold in a space form ...
Zhu Jonathan J.
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Potential Theory on Gromov Hyperbolic Spaces
Analysis and Geometry in Metric Spaces, 2022 Gromov hyperbolic spaces have become an essential concept in geometry, topology and group theory. Herewe extend Ancona’s potential theory on Gromov hyperbolic manifolds and graphs of bounded geometry to a large class of Schrödinger operators on Gromov ...
Kemper Matthias, Lohkamp Joachim
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Three candidate plurality is stablest for small correlations
Forum of Mathematics, Sigma, 2021 Using the calculus of variations, we prove the following structure theorem for noise-stable partitions: a partition of n-dimensional Euclidean space into m disjoint sets of fixed Gaussian volumes that maximise their noise stability must be $(m-1 ...
Steven Heilman, Alex Tarter
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Stable anisotropic minimal hypersurfaces in $\mathbf {R}^{4}$
Forum of Mathematics, Pi, 2023 We show that a complete, two-sided, stable immersed anisotropic minimal hypersurface in $\mathbf {R}^4$ has intrinsic cubic volume growth, provided the parametric elliptic integral is $C^2$ -close to the area functional.
Otis Chodosh, Chao Li
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GLOBAL NEARLY-PLANE-SYMMETRIC SOLUTIONS TO THE MEMBRANE EQUATION
Forum of Mathematics, Pi, 2020 We prove that any simple planar travelling wave solution to the membrane equation in spatial dimension $d\geqslant 3$ with bounded spatial extent is globally nonlinearly stable under sufficiently small compactly supported perturbations, where the ...
LEONARDO ABBRESCIA +1 more
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The rigidity of embedded constant mean curvature surfaces [PDF]
, 2007 We study the rigidity of complete, embedded constant mean curvature surfaces in R^3. Among other things, we prove that when such a surface has finite genus, then intrinsic isometries of the surface extend to isometries of R^3 or its isometry group ...
Meeks III, William H. +1 more
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CMC Spheres in the Heisenberg Group
Analysis and Geometry in Metric Spaces, 2019 We study a family of spheres with constant mean curvature (CMC) in the Riemannian Heisenberg group H1. These spheres are conjectured to be the isoperimetric sets of H1. We prove several results supporting this conjecture.
Franceschi Valentina +2 more
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Minimal surfaces with non-trivial geometry in the three-dimensional Heisenberg group
Complex Manifolds, 2022 We study symmetric minimal surfaces in the three-dimensional Heisenberg group Nil3 using the generalized Weierstrass type representation, the so-called loop group method.
Dorfmeister Josef F. +2 more
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International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 18, Page 913-948, 2004., 2004 We obtain global estimates for the modulus, interior gradient estimates, and boundary Hölder continuity estimates for solutions u to the capillarity problem and to the Dirichlet problem for the mean curvature equation merely in terms of the mean curvature, together with the boundary contact angle in the capillarity problem and the boundary values in ...
Fei-Tsen Liang
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On the moduli space of superminimal surfaces in spheres
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 44, Page 2803-2827, 2003., 2003 Using a birational correspondence between the twistor space of S2n and projective space, we describe, up to birational equivalence, the moduli space of superminimal surfaces in S2n of degree d as curves of degree d in projective space satisfying a certain differential system.
Luis Fernández
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