Quasisymmetric Koebe Uniformization
Metric Geometry
2011-09-16 v1 Complex Variables
Abstract
We study a quasisymmetric version of the classical Koebe uniformization theorem in the context of Ahlfors regular metric surfaces. In particular, we prove that an Ahlfors 2-regular metric surface X homeomorphic to a finitely connected domain in the standard 2-sphere is quasisymmetrically equivalent to a circle domain if and only if X is linearly locally connected and its completion is compact. We also give a counterexample in the countably connected case.
Cite
@article{arxiv.1109.3441,
title = {Quasisymmetric Koebe Uniformization},
author = {Sergei Merenkov and Kevin Wildrick},
journal= {arXiv preprint arXiv:1109.3441},
year = {2011}
}
Comments
46 pages, 8 figures