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.
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页码：93 / 107
页数：15
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