A geometric proof of some inequalities involving mixed volumes
type: Item
instance of: scholarly article
title: A geometric proof of some inequalities involving mixed volumes
zbMATH Open document ID: 0977.52016
author: Mathieu Meyer
author: Shlomo Reisner
published in: Beiträge zur Algebra und Geometrie
publication date: 2000-09-13T00:00:00Z
full work available at URL: https://eudml.org/doc/232249
full work available at URL: 4.html
review text: Using spherical harmonics, \textit{R. Schneider} [Mathematika 36, No. 1, 50-59 (1989; Zbl 0671.52008)] and \textit{P. R. Goodey} and \textit{H. Groemer} [Proc. Am. Math. Soc. 109, No. 4, 1103-1114 (1990; Zbl 0699.52001)] proved stability versions of special cases of the Alexandrov-Fenchel inequalities. Here a proof is given which uses the Blaschke-Santaló inequality and a variational argument instead of spherical harmonics.
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A39
zbMATH DE Number: 1505607
zbMATH Keywords: stability
zbMATH Keywords: Alexandrov-Fenchel inequalities
zbMATH Keywords: Blaschke-Santaló inequality
reviewed by: Erhard Heil
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1505607