Affine isoperimetric inequalities in the functional Orlicz-Brunn-Minkowski theory

被引：21

作者：

Caglar, Umut ^{[1
]}

Ye, Deping ^{[2
]}

机构：

[1] Florida Int Univ, Dept Math & Stat, Miami, FL 33199 USA

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

来源：

ADVANCES IN APPLIED MATHEMATICS | 2016年 / 81卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Affine isoperimetric inequalities; Affine surface area; Functional inequality; Geometrization of probability; Geominimal surface area; L-p affine surface area; L-p-Brunn-Minkowski theory; L-p geominimal surface area; Orlicz-Brunn-Minkowski theory; Orlicz-Minkowski inequality; The Blaschke-Santalo inequality; CONCAVE; DIVERGENCE; SOBOLEV;

D O I：

10.1016/j.aam.2016.06.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we develop a basic theory of Orlicz affine and geominimal surface areas for convex and epsilon-concave functions. We prove some basic properties for these newly introduced functional affine invariants and establish related functional affine isoperimetric inequalities as well as functional Santalo type inequalities. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：78 / 114

页数：37

共 39 条

[1]

[Anonymous], 1923, GRUNDLEHREN MATH WIS

[2]

[Anonymous], 1996, PRINCETON MATH SER

[3]

[Anonymous], 1939, Leningrad State Univ. Annals Uchenye Zapiski Math. Ser.

[4] The Santalo point of a function, and a functional form of the Santalo inequality [J].