Results 1 to 10 of about 73 (58)
Symmetric solutions to isoperimetric problems for polytopes
Applied Geometry And Discrete Mathematics, 1991 P. Filliman
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Minimality of polytopes in a nonlocal anisotropic isoperimetric problem [PDF]
Nonlinear Analysis, 2021 We consider the minimization of an energy functional given by the sum of a crystalline perimeter and a nonlocal interaction of Riesz type, under volume constraint. We show that, in the small mass regime, if the Wulff shape of the anisotropic perimeter has certain symmetry properties, then it is the unique global minimizer of the total energy.
Bonacini, Marco +2 more
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Discrete isoperimetric problems in spaces of constant curvature [PDF]
Mathematika, Volume 69, Issue 1, Page 33-50, January 2023., 2022 The aim of this paper is to prove isoperimetric inequalities for simplices and polytopes with d+2$d+2$ vertices in Euclidean, spherical and hyperbolic d‐space.
Bushra Basit, Z. Lángi
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Convergence of the Riemannian Langevin Algorithm [PDF]
arXiv.org, 2022 We study the Riemannian Langevin Algorithm for the problem of sampling from a distribution with density ν with respect to the natural measure on a manifold with metric g.
Khashayar Gatmiry, S. Vempala
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The extremals of the Alexandrov–Fenchel inequality for convex polytopes [PDF]
Acta Mathematica, 2020 The Alexandrov-Fenchel inequality, a far-reaching generalization of the classical isoperimetric inequality to arbitrary mixed volumes, lies at the heart of convex geometry.
Yair Shenfeld, R. Handel
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Shadows of convex bodies [PDF]
, 1989 It is proved that if C is a convex body in Rn then C has an affine image C (of nonzero volume) so that if P is any 1-codimensional orthogonal projection, |PCa > 1Žcl(n-l)/n It is also shown that there is a pathological body, K, all of whose orthogonal ...
K. Ball
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The isoperimetric problem for $3$-polytopes with six vertices
, 2019 We prove that the regular octahedron has the minimal surface area among 3-polytopes of given volume and having at most six vertices.
Böröczky, Károly J., Kovács, Ágnes
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The edge-isoperimetric problem on the 600-vertex regular solid
, 2003 Between 1963 and 1979 the edge-isoperimetric problem was solved on the graphs of all regular convex polytopes except the four-dimensional one with 600 vertices.
L. H. Harper, D. Dreier
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, 2018 This book consists of contributions from experts, presenting a fruitful interplay between different approaches to discrete geometry. Most of the chapters were collected at the conference “Geometry and Symmetry” in Veszprém, Hungary from 29 June to 3 July
Deza, Antoine +2 more
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Floating Bodies and Approximation - Part 3
, 2019 Presented on December 11, 2019 at 3:45 p.m. in the Bill Moore Student Success Center, Press Rooms A & B, Georgia Tech.Workshop in Convexity and Geometric Aspects of Harmonic AnalysisElisabeth Werner, Case Western Reserve University, Department of ...
Werner, Elisabeth
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