LYZ ellipsoid and Petty projection body for log-concave functions

被引：24

作者：

Fang, Niufa ^{[1
,2
]}

Zhou, Jiazu ^{[1
,3
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

[2] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China

[3] Wuhan Univ Sci & Technol, Coll Sci, Wuhan 430081, Hubei, Peoples R China

来源：

ADVANCES IN MATHEMATICS | 2018年 / 340卷

关键词：

LYZ ellipsoid; Petty projection body; log-concave function; The first variation; Valuation; BRUNN-MINKOWSKI; AFFINE; INEQUALITY; VALUATIONS; DIVERGENCE; STABILITY; BODIES; FORMS;

D O I：

10.1016/j.aim.2018.10.029

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aims of this paper are to develop the LYZ ellipsoid and Petty projection body for log-concave functions, which correspond to the LYZ ellipsoid and Petty projection body for convex bodies when restricted to the subclass of characteristic functions. Moreover, the continuous, SL(n) contravariant valuation on a subclass of log-concave functions is classified. (C) 2018 Published by Elsevier Inc.

引用

页码：914 / 959

页数：46

共 75 条

[1] John's Ellipsoid and the Integral Ratio of a Log-Concave Function [J].