The log-Brunn-Minkowski inequality

被引：233
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.
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页码：1974 / 1997
页数：24
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