Mean width inequalities for isotropic measures

被引：14
作者：
Li, Ai-Jun [1 ]
Leng, Gangsong [2 ]
机构：
[1] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454000, Peoples R China
[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
MATHEMATISCHE ZEITSCHRIFT | 2012年 / 270卷 / 3-4期
基金：
中国国家自然科学基金;
关键词：
Mean width inequality; Isotropic measure; l-norm; Ball-Barthe inequality; BRASCAMP-LIEB INEQUALITIES; JOHNS DECOMPOSITION; VOLUME INEQUALITIES; ELLIPSOIDS; POSITIONS;
D O I：
10.1007/s00209-011-0843-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we establish Barthe's mean width inequalities for continuous isotropic measures by a direct approach rather than using the Brascamp-Lieb inequality. The following results are obtained: among the convex hulls of the support of isotropic measures on S (n-1), the regular simplex inscribed in the Euclidean unit ball has maximal a""-norm; in the dual situation, there is a reverse result for their polar bodies. Moreover, the case of even isotropic measures is also investigated.
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页码：1089 / 1110
页数：22
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