Weak Capacity and Modulus Comparability in Ahlfors Regular Metric Spaces-Reference-Cited by-同舟云学术

Weak Capacity and Modulus Comparability in Ahlfors Regular Metric Spaces

Published:2016-12-30 Issue:1 Volume:4 Page:
ISSN:2299-3274
Container-title:Analysis and Geometry in Metric Spaces
language:
Short-container-title:

Author:

Lindquist Jeff¹

Affiliation:

1. 1Department of Mathematics, University of California, Los Angeles, Box 95155, Los Angeles, CA, 90095-1555, USA

Abstract

AbstractLet (Z, d, μ) be a compact, connected, Ahlfors Q-regular metric space with Q > 1. Using a hyperbolic filling of Z,we define the notions of the p-capacity between certain subsets of Z and of theweak covering p-capacity of path families Γ in Z.We show comparability results and quasisymmetric invariance.As an application of our methodswe deduce a result due to Tyson on the geometric quasiconformality of quasisymmetric maps between compact, connected Ahlfors Q-regular metric spaces.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Geometry and Topology,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/agms-2016-0019/pdf

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