Weak Capacity and Modulus Comparability in Ahlfors Regular Metric Spaces

Jeff Lindquist. "Weak Capacity and Modulus Comparability in Ahlfors Regular Metric Spaces." Analysis and Geometry in Metric Spaces 4.1 (2016): 399-424. <http://eudml.org/doc/288087>.

@article{JeffLindquist2016,
abstract = {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.},
author = {Jeff Lindquist},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Weak capacity; weak covering capacity; modulus; quasisymmetry; quasi-isometry; Ahlfors regular metric space; Gromov hyperbolic metric space; Ahlfors regular conformal dimension; weak capacity; Ahlfors regular metric space},
language = {eng},
number = {1},
pages = {399-424},
title = {Weak Capacity and Modulus Comparability in Ahlfors Regular Metric Spaces},
url = {http://eudml.org/doc/288087},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Jeff Lindquist
TI - Weak Capacity and Modulus Comparability in Ahlfors Regular Metric Spaces
JO - Analysis and Geometry in Metric Spaces
PY - 2016
VL - 4
IS - 1
SP - 399
EP - 424
AB - 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.
LA - eng
KW - Weak capacity; weak covering capacity; modulus; quasisymmetry; quasi-isometry; Ahlfors regular metric space; Gromov hyperbolic metric space; Ahlfors regular conformal dimension; weak capacity; Ahlfors regular metric space
UR - http://eudml.org/doc/288087
ER -