The dual Orlicz-Brunn-Minkowski theory

被引：85

作者：

Gardner, Richard J. ^{[1
]}

Hug, Daniel ^{[2
]}

Weil, Wolfgang ^{[2
]}

Ye, Deping ^{[3
]}

机构：

[1] Western Washington Univ, Dept Math, Bellingham, WA 98225 USA

[2] Karlsruhe Inst Technol, Dept Math, D-76128 Karlsruhe, Germany

[3] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 430卷 / 02期

基金：

美国国家科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

Star body; Orlicz-Brunn-Minkowski theory; M-addition; Orlicz addition; Radial addition; Brunn-Minkowski inequality; BUSEMANN-PETTY PROBLEM; MIXED VOLUMES; CONVEX; BODIES; SETS;

D O I：

10.1016/j.jmaa.2015.05.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A first step towards a dual Orlicz-Brunn-Minkowski theory for star sets was taken by Zhu, Zhou, and Xue [44,45]. In this essentially independent work we provide a more general framework and results. A radial Orlicz addition of two or more star sets is proposed and a corresponding dual Orlicz-Brunn-Minkowski inequality is established. Based on a radial Orlicz linear combination of two star sets, a formula for the dual Orlicz mixed volume is derived and a corresponding dual Orlicz-Minkowski inequality proved. The inequalities proved yield as special cases the precise duals of the conjectured log-Brunn-Minkowski and log-Minkowski inequalities of Boroczky, Lutwak, Yang, and Zhang. A new addition of star sets called radial M-addition is also introduced and shown to relate to the radial Orlicz addition. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：810 / 829

页数：20

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