On the Brunn-Minkowski theorem
type: Item
instance of: scholarly article
title: On the Brunn-Minkowski theorem
zbMATH Open document ID: 0652.52009
DOI: 10.1007/BF00181500
published in: Geometriae Dedicata
publication date: 1988-01-01T00:00:00Z
review text: Let \(K_ 1\) and \(K_ 2\) be n-dimensional convex bodies which satisfy for some \(\alpha\in]0,1[\) and some \(\epsilon \in [0,+\infty [\) the inequality \[ V(\alpha K_ 1+(1-\alpha)K_ 2)^{1/n}\leq \alpha V(K_ 1)^{1/n}+(1-\alpha)V(K_ 2)^{1/n}+\epsilon \quad, \] where V denotes the volume. The problem investigated in the present paper is whether \(K_ 1\) and \(K_ 2\) are in some sense homothetic. Several theorems that answer this question associated with the Brunn-Minkowski inequality are proved.
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 4063947
zbMATH Keywords: stability
zbMATH Keywords: volume
zbMATH Keywords: homothetic
zbMATH Keywords: Brunn-Minkowski inequality
author: Helmut Groemer
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00181500
OpenAlex ID: W1985840539
description: scientific article; zbMATH DE number 4063947