Isoperimetric problem for exponential measure on the plane with l1-metric

被引：0

作者：

Strzelecka, Marta ^{[1
]}

机构：

[1] Univ Warsaw, Fac Math Informat & Mech, Banacha 2, PL-02097 Warsaw, Poland

来源：

POSITIVITY | 2017年 / 21卷 / 04期

关键词：

Isoperimetric inequality; Exponential measure; Symmetrisation; DISTRIBUTIONS; SPACES;

D O I：

10.1007/s11117-017-0476-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a solution to the isoperimetric problem for the exponential measure on the plane with the -metric. As it turns out, among all sets of a given measure, the simplex or its complement (i.e. the ball in the -metric or its complement) has the smallest boundary measure. The proof is based on a symmetrisation (along the sections of equal -distance from the origin).

引用

页码：1425 / 1438

页数：14

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