Results 1 to 10 of about 28 (27)
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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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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Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings. [PDF]
Calc Var Partial Differ Equ, 2022 Del Nin G, Petrache M.
europepmc +1 more source
Tropical Ehrhart theory and tropical volume. [PDF]
Res Math Sci, 2020 Loho G, Schymura M.
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Dual Loomis-Whitney Inequalities via Information Theory. [PDF]
Entropy (Basel), 2019 Hao J, Jog V.
europepmc +1 more source
Error Resilient Space Partitioning. [PDF]
Discrete Comput GeomDunkelman O +6 more
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Some of the next articles are maybe not open access.
Isoperimetric problems for polytopes with a given number of vertices
Mathematika, 1996The authors address the following problem: among all convex \(d\)-polytopes \(P\) with \(n\) vertices and prescribed volume or minimal edge-length, for which is the intrinsic \(i\)-volume \(V_i(P)\) minimal? For fixed volume, the case of the simplex \((n=d+1)\) has been settled by \textit{H.
Böröczky, Károly +1 more
openaire +4 more sources
Sharp affine isoperimetric inequalities for the volume decomposition functionals of polytopes
Advances in Mathematics, 2021Ge Xiong
exaly
Higher-Order Noether’s Theorem for Isoperimetric Variational Problems
Journal of Optimization Theory and Applications, 2023Matheus Lazo
exaly