The log-Brunn-Minkowski inequality

被引：227

作者：

Boeroeczky, Karoly J. ^{[2
]}

Lutwak, Erwin ^{[1
]}

Yang, Deane ^{[1
]}

Zhang, Gaoyong ^{[1
]}

机构：

[1] NYU, Polytech Inst, Brooklyn, NY USA

[2] Hungarian Acad Sci, Alfred Renyi Inst Math, H-1051 Budapest, Hungary

来源：

ADVANCES IN MATHEMATICS | 2012年 / 231卷 / 3-4期

基金：

美国国家科学基金会;

关键词：

Brunn-Minkowski inequality; Brunn-Minkowski-Firey inequality; Minkowski mixed-volume inequality; Minkowski-Firey L-p-combinations; VOLUME INEQUALITIES; FIREY THEORY; AFFINE; BODIES; CLASSIFICATION; CURVATURE; SHAPES;

D O I：

10.1016/j.aim.2012.07.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For origin-symmetric convex bodies the unit balls of finite dimensional Banach spaces) it is conjectured that there exist a family of inequalities each of which is stronger than the classical Brunn-Minkowski inequality and a family of inequalities each of which is stronger than the classical Minkowski mixed-volume inequality. It is shown that these two families of inequalities are "equivalent" in that once either of these inequalities is established, the other Must follow as a consequence. All of the conjectured inequalities are established for plane convex bodies. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1974 / 1997

页数：24

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