Cone-volume measure of general centered convex bodies

被引：65

作者：

Boeroeczky, Karoly J. ^{[1
]}

Henk, Martin ^{[2
]}

机构：

[1] Hungarian Acad Sci, Alfred Renyi Inst Math, H-1053 Budapest, Hungary

[2] Tech Univ Berlin, Inst Math, Sekr Ma 4-1,Str 17 Juni 136, D-10623 Berlin, Germany

来源：

ADVANCES IN MATHEMATICS | 2016年 / 286卷

关键词：

Cone-volume measure; Subspace concentration condition; U-functional Centro-affine inequalities; log-Minkowski problem; L-P-Minkowsld problem; Centroid; Polytope; MINKOWSKI PROBLEM; SURFACE MEASURE; INEQUALITIES; INVARIANT; SPHERE;

D O I：

10.1016/j.aim.2015.09.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the cone-volume measure of a convex body with centroid at the origin satisfies the subspace concentration condition. This extends former results obtained in the discrete as well as in the symmetric case and implies, among others, a conjectured best possible inequality for the U-functional of a convex body. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：703 / 721

页数：19

共 46 条

[1]

[Anonymous], 2012, DIVERGENCE THEOREM S

[2]

[Anonymous], 2007, GRUNDLEHREN MATH WIS

[3]

[Anonymous], 1996, PRINCETON MATH SER

[4] LOGARITHMICALLY CONCAVE FUNCTIONS AND SECTIONS OF CONVEX-SETS IN RN [J].

BALL, K .

STUDIA MATHEMATICA, 1988, 88 (01) :69-84

[5]

BALL K, 1991, J LOND MATH SOC, V44, P351

[6]

Barthe F, 2004, LECT NOTES MATH, V1850, P53

[7] On a reverse form of the Brascamp-Lieb inequality [J].

Barthe, F .

INVENTIONES MATHEMATICAE, 1998, 134 (02) :335-361

[8] A probabilistic approach to the geometry of the lnp-ball [J].

Barthe, F ;

Guédon, O ;

Mendelson, S ;

Naor, A .

ANNALS OF PROBABILITY, 2005, 33 (02) :480-513

[9] Invariances in variance estimates [J].

Barthe, F. ;

Cordero-Erausquin, D. .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2013, 106 :33-64

[10] The Brascamp-Lieb inequalities: Finiteness, structure and extremals [J].

Bennett, Jonathan ;

Carbery, Anthony ;

Christ, Michael ;

Tao, Terence .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 2007, 17 (05) :1343-1415

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