Orlicz mixed quermassintegrals
type: Item
instance of: scholarly article
title: Orlicz mixed quermassintegrals
zbMATH Open document ID: 1328.52003
author: Ge Xiong
author: Zou Du
published in: Science China. Mathematics
publication date: 2015-03-26T00:00:00Z
review text: The authors extend the notion of mixed quermassintegrals from classical Brunn-Minkowski theory to Orlicz Brunn-Minkowski theory, calling it Orlicz mixed quermassintegrals. On that base they succeed to establish respective analogues of classical notions like Cauchy-Kubota formula, Minkowski's isoperimetric inequality, the Brunn-Minkowski inequality, difference bodies and further ones. They also pose an interesting problem related to the conjectured log-Minkowski inequality.
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52A39
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A22
zbMATH DE Number: 6419679
zbMATH Keywords: Orlicz Brunn-Minkowski theory
zbMATH Keywords: quermassintegral
zbMATH Keywords: Minkowski's isoperimetric inequality
zbMATH Keywords: integral geometry
MaRDI profile type: Publication
full work available at URL: s11425-014-4812-4
OpenAlex ID: W2261105716
cites work: Q5769211
cites work: The log-Brunn-Minkowski inequality
cites work: The logarithmic Minkowski problem
cites work: The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
cites work: $p$-Means of Convex Bodies.
cites work: A stability result for mean width of \(L_{p}\)-centroid bodies
cites work: Q3409343
cites work: The Orlicz-Brunn-Minkowski theory: a general framework, additions, and inequalities
cites work: Convex and Discrete Geometry
cites work: The even Orlicz Minkowski problem
cites work: Projection problems for symmetric polytopes
cites work: General affine surface areas
cites work: The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
cites work: The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
cites work: A new ellipsoid associated with convex bodies
cites work: \(L_ p\) affine isoperimetric inequalities.
cites work: On the $L_{p}$-Minkowski problem
cites work: $L_p$ John Ellipsoids
cites work: Orlicz projection bodies
cites work: Orlicz centroid bodies
cites work: Relative entropy of cone measures and L p centroid bodies
cites work: Q4000065
cites work: Q4024093
cites work: Fourier transform and Firey projections of convex bodies
cites work: Q4787438
cites work: Surface bodies and \(p\)-affine surface area
cites work: Q5287551
cites work: The discrete planar \(L_0\)-Minkowski problem
cites work: Q4716272
cites work: New \(L_p\) affine isoperimetric inequalities
cites work: Rényi divergence and \(L_p\)-affine surface area for convex bodies
cites work: Extremum problems for the cone volume functional of convex polytopes
cites work: Centroid bodies and comparison of volumes
cites work: Orlicz-John ellipsoids
DOI: 10.1007/S11425-014-4812-4
description: scientific article; zbMATH DE number 6419679