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.
@article{bwmeta1.element.doi-10_1515_agms-2016-0019,
author = {Jeff Lindquist},
title = {Weak Capacity and Modulus Comparability in Ahlfors Regular Metric Spaces},
journal = {Analysis and Geometry in Metric Spaces},
volume = {4},
year = {2016},
zbl = {06682298},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2016-0019}
}
Jeff Lindquist. Weak Capacity and Modulus Comparability in Ahlfors Regular Metric Spaces. Analysis and Geometry in Metric Spaces, Tome 4 (2016) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2016-0019/