Geometric implications of the poincare inequality

被引：35

作者：

Korte, Riikka ^{[1
]}

机构：

[1] Aalto Univ, Inst Math, FIN-02015 Helsinki, Finland

来源：

RESULTS IN MATHEMATICS | 2007年 / 50卷 / 1-2期

关键词：

poincare inequality; quasiconvexity; capacity; modulus; metric spaces;

D O I：

10.1007/s00025-006-0237-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this work is to prove the following result: If a doubling metric measure space supports a weak (1, p)-Poincare inequality with p sufficiently small, then annuli are almost quasiconvex. We also obtain estimates for the Hausdorff s-content and the diameter of the spheres. Mathematics Subject Classification (2000). Primary 46E35; Secondary 31C15.

引用

页码：93 / 107

页数：15

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