The Sharp Sobolev Inequality on Metric Measure Spaces with Lower Ricci Curvature Bounds

被引：9

作者：

Profeta, Angelo ^{[1
]}

机构：

[1] Univ Bonn, Inst Appl Math, D-53115 Bonn, Germany

来源：

POTENTIAL ANALYSIS | 2015年 / 43卷 / 03期

关键词：

Sharp Sobolev inequality; Nash inequality; Metric measure spaces; Curvature-dimension condition; GEOMETRY;

D O I：

10.1007/s11118-015-9485-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the sharp Sobolev inequality as known for Riemannian manifolds with a positive lower bound on the Ricci curvature holds in the same form for metric measure spaces satisfying the RCD*(K, N) condition for positive K.

引用

页码：513 / 529

页数：17

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