A Brunn-Minkowski inequality for the Monge-Ampere eigenvalue

被引：21

作者：

Salani, P ^{[1
]}

机构：

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

来源：

ADVANCES IN MATHEMATICS | 2005年 / 194卷 / 01期

关键词：

Brunn-Minkowski inequality; Monge-Ampere equation; eigenvalue; intimal convolution;

D O I：

10.1016/j.aim.2004.05.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a Brunn-Minkowski-type inequality 2 for the eigenvalue Λ of the Monge-Ampere operator: Λ(-1/2n) is concave in the class of C-+(2) domains in R-n endowed with Minkowski addition. The equality case is explicitly described too. The main device of the proof is a notion of addition for convex functions, called infimal convolution, which corresponds to the Minkowski addition of the graphs of the involved functions. © 2004 Elsevier Inc. All rights reserved.

引用

页码：67 / 86

页数：20

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