The Orlicz-Minkowski problem for polytopes
type: Item
instance of: scholarly article
title: The Orlicz-Minkowski problem for polytopes
zbMATH Open document ID: 1483.52005
author: Chu Wang
author: Meiyue Jiang
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2021-12-08T00:00:00Z
review text: The classical Minkowski problem and various modern versions of it, known as Minkowski-type problems, are crucial in the study of convex bodies throughout the 20th and 21st century and even more so in the last few decades. Some of the most influential Minkowski-type problems include the \(L_p\) Minkowski problem (which contains the well-known logarithmic Minkowski problem) and the recently posed dual Minkowski problems. These problems, with enough regularity assumed, reduce to the study of a family of Monge-Ampere type equations. The uniqueness of these solutions are often tied to isoperimetric inequalities and spetrum analysis of certain second order nonlinear elliptic operators. The current paper establishes some existence result for the Orlicz Minkowski problem. It uses a variational approach and studies particularly the discrete case.
reviewed by: Yiming Zhao
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 49J20
zbMATH DE Number: 7440390
zbMATH Keywords: polytopes
zbMATH Keywords: Orlicz-Minkowski problem
MaRDI profile type: Publication
full work available at URL: dcdss.2021043
OpenAlex ID: W3159604231
cites work: Self-similar solutions for the anisotropic affine curve shortening problem
cites work: On the discrete logarithmic Minkowski problem
cites work: The logarithmic Minkowski problem
cites work: \(L_p\) Minkowski problem with not necessarily positive data
cites work: On the regularity of the solution of then-dimensional Minkowski problem
cites work: The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
cites work: The two dimensional \(L_p\) Minkowski problem and nonlinear equations with negative exponents
cites work: The even Orlicz Minkowski problem
cites work: On the Orlicz Minkowski problem for polytopes
cites work: On the \(L_{p}\) Minkowski problem for polytopes
cites work: Remarks on the 2-Dimensional Lp-Minkowski Problem
cites work: 2\(\pi\)-periodic self-similar solutions for the anisotropic affine curve shortening problem
cites work: \(2\pi\)-periodic self-similar solutions for the anisotropic affine curve shortening problem. II
cites work: Polar correspondence with respect to a convex region
cites work: On Differential Geometry in the Large, I (Minkowski's Problem)
cites work: Rotationally symmetric solutions to the \(L_p\)-Minkowski problem
cites work: The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
cites work: On the $L_{p}$-Minkowski problem
cites work: The Weyl and Minkowski problems in differential geometry in the large
cites work: The discrete planar \(L_0\)-Minkowski problem
cites work: The logarithmic Minkowski problem for polytopes
cites work: The centro-affine Minkowski problem for polytopes
cites work: The \(L_p\) Minkowski problem for polytopes for \(0 < p < 1\)
cites work: The Lp Minkowski problem for polytopes for p<0
DOI: 10.3934/DCDSS.2021043
description: scientific article; zbMATH DE number 7440390