Weak Capacity and Modulus Comparability in Ahlfors Regular Metric Spaces

• Autorzy: Jeff Lindquist
• Języki publikacji: EN

Abstrakty

EN

Let (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.

Słowa kluczowe

EN

Weak capacity; weak covering capacity; modulus; quasisymmetry; quasi-isometry; Ahlfors regularmetric space; Gromov hyperbolic metric space; Ahlfors regular conformal dimension

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2016
• Tom: 4
• Numer: 1

Daty

otrzymano

2016-08-05

zaakceptowano

2016-12-20

online

2016-12-30

Twórcy

autor

Jeff Lindquist

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

Identyfikatory

DOI

10.1515/agms-2016-0019