A mass transportation approach to quantitative isoperimetric inequalities

被引：248

作者：

Figalli, A. ^{[1
]}

Maggi, F. ^{[2
]}

Pratelli, A. ^{[3
]}

机构：

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

[2] Univ Firenze, Dipartimento Matemat U Dini, I-50134 Florence, Italy

[3] Univ Pavia, Dipartimento Matemat, I-27100 Pavia, Italy

来源：

INVENTIONES MATHEMATICAE | 2010年 / 182卷 / 01期

关键词：

SOBOLEV INEQUALITY; SHARP SOBOLEV; MINKOWSKI; UNIQUENESS; STABILITY; SURFACE; THEOREM;

D O I：

10.1007/s00222-010-0261-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A sharp quantitative version of the anisotropic isoperimetric inequality is established, corresponding to a stability estimate for the Wulff shape of a given surface tension energy. This is achieved by exploiting mass transportation theory, especially Gromov's proof of the isoperimetric inequality and the Brenier-McCann Theorem. A sharp quantitative version of the Brunn-Minkowski inequality for convex sets is proved as a corollary.

引用

页码：167 / 211

页数：45

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[2]

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[3]

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[4]

[Anonymous], 1985, SOBOLEV INEQUALITIES