Dual cyclic Brunn-Minkowski inequalities
type: Item
instance of: scholarly article
title: Dual cyclic Brunn-Minkowski inequalities
zbMATH Open document ID: 1331.52016
author: Changjian Zhao
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2015-11-02T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1442364586
review text: An application of Minkowski and Hölder inequalities to functions on the sphere \(\mathbb S^{n-1}\) led the author to a new interpolation type inequality between norms \(L_r\), \(L_s\), \(L_t\) for \(r\), \(s\), \(t \in \mathbb R\). This was furthermore used to derive new Brunn-Minkowski type inequalities for dual quermassintegrals of star bodies in \(\mathbb{R}^n\) considered successively with the Minkowski addition, and radial Blaschke addition, and harmonic Blaschke addition. The author's new Brunn-Minkowski inequalities generalize known dual Brunn-Minkowski inequalities for the radial additions listed above, two of them dating back to Lutwak's paper on dual mixed volumes from 1975 where many Brunn-Minkowski duality questions originate.
reviewed by: Alina Stancu
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A30
zbMATH DE Number: 6502894
zbMATH Keywords: dual Brunn-Minkowski inequality
zbMATH Keywords: harmonic Blaschke addition
zbMATH Keywords: radial Blaschke addition
zbMATH Keywords: radial Minkowski addition
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6502894