Results in Mathematics

, Volume 50, Issue 1, pp 93–107

Geometric Implications of the Poincaré Inequality

Article

DOI: 10.1007/s00025-006-0237-x

Cite this article as:
Korte, R. Result. Math. (2007) 50: 93. doi:10.1007/s00025-006-0237-x

Abstract.

The purpose of this work is to prove the following result: If a doubling metric measure space supports a weak (1, p)–Poincaré 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 

Keywords.

Poincaré inequality quasiconvexity capacity modulus metric spaces 

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Institute of MathematicsHelsinki University of TechnologyHelsinkiFinland