Results 31 to 40 of about 81,686,599 (65)
Minimal periodic foams with fixed inradius
Mathematika, Volume 71, Issue 2, April 2025.Abstract In this note, we show existence and regularity of periodic tilings of the Euclidean space into equal cells containing a ball of fixed radius, which minimize either the classical or the fractional perimeter. We also discuss some qualitative properties of minimizers in dimensions 3 and 4.
Annalisa Cesaroni, Matteo Novaga
wiley +1 more source
Shortest closed curve to contain a sphere in its convex hull
Bulletin of the London Mathematical Society, Volume 56, Issue 7, Page 2472-2482, July 2024.Abstract We show that in Euclidean 3‐space any closed curve which contains the unit sphere within its convex hull has length L⩾4π$L\geqslant 4\pi$, and characterize the case of equality. This result generalizes the authors' recent solution to a conjecture of Zalgaller. Furthermore, for the analogous problem in n$n$ dimensions, we include the estimate L⩾
Mohammad Ghomi, James Wenk
wiley +1 more source
NUMBER OF SIMPLICIAL NEIGHBORLY D-POLYTOPES WITH D+3 VERTICES [PDF]
, 1973 In this paper is proved a formula for the number of simplicial neighbourly d-polytopes with d + 3 vertices, when d is ...
MCMULLEN, P, ALTSHULE, A
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Isoperimetric problems for zonotopes [PDF]
, 2023 Shephard (Canad. J. Math. 26: 302-321, 1974) proved a decomposition theorem for zonotopes yielding a simple formula for their volume. In this note we prove a generalization of this theorem yielding similar formulas for their intrinsic volumes.
Lángi, Zsolt, Joós, Antal
core +1 more source
NUMBER OF NEIGHBORLY D-POLYTOPES WITH D+3 VERTICES [PDF]
, 1974 In this paper is proved a formula for the number of neighbourly d-polytopes with d + 3 vertices, when d is ...
MCMULLEN, P
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Non-Local Isoperimetric Problems [PDF]
, 2014 37 pagesWe characterize the volume-constrained minimizers of a nonlocal free energy given by the difference of the $t$-perimeter and the $s$-perimeter, with $s$ smaller than $t$.
Ruffini, Berardo +3 more
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, 2019 K-polytopes is a superproblem of well known k-means.Instead of points, think of choosing central objects as general (possibly non-convex and piecewise linear) shapes, or q-dimensional polytopes in n-dimensions.
Yigit Oktar (6586790)
core +1 more source
Randomly generated polytopes for testing mathematical programming algorithms [PDF]
Randomly generated polytopes are used frequently to test and compare algorithms for a variety of mathematical programming problems. These polytopes are constructed by generating linear inequality constraints with coefficients drawn independently from a ...
Dam, W.B. van
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A tropical isoperimetric inequality
, 2017 arXiv:1611.04148International audienceWe introduce tropical analogues of the notion of volume of polytopes, leading to a tropical version of the (discrete) classical isoperimetric inequality.
Joswig, Michael +2 more
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Discrete isoperimetric problems in spaces of constant curvature
, 2022 The aim of this paper is to prove isoperimetric inequalities for simplices and polytopes with $d+2$ vertices in Euclidean, spherical and hyperbolic $d$-space.
Langi, Zsolt, Basit, Bushra
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