Results 21 to 30 of about 73 (58)

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

Projection bodies

, 2009
Ziel dieser Diplomarbeit ist es in möglichst geschlossener Darstellung die grundlegenden Eigenschaften von Projektionkörpern zu präsentieren und einige erstaunliche Beispiele ihrer Verwendung in der konvexen und stochastischen Geometrie zu geben.Ein ...
Wannerer, Thomas
core  

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.
europepmc   +1 more source

On the higher-order affine isoperimetric and isocapacitary inequalities

Understanding the size and shape of convex bodies is fundamental in many geometric problems and plays an important role in applications. Commonly used measurements for convex bodies include volume, surface area, diameters etc; and polytopes, Euclidean ...
Zhou, Xia
core  

Dual Loomis-Whitney Inequalities via Information Theory. [PDF]

Entropy (Basel), 2019
Hao J, Jog V.
europepmc   +1 more source

The Minkowski problem for polytopes

, 2004
Daniel A. Klain
semanticscholar   +1 more source

A new affine invariant for polytopes and Schneider’s projection problem

, 2001
E. Lutwak, Deane Yang, Gaoyong Zhang
semanticscholar   +1 more source

Isoperimetric Estimates on Sierpinski Gasket Type Fractals

, 1999
R. Strichartz
semanticscholar   +1 more source