Quasisymmetric Koebe Uniformization
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 2regular metric surface X homeomorphic to a finitely connected domain in the standard 2sphere 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2011
 arXiv:
 arXiv:1109.3441
 Bibcode:
 2011arXiv1109.3441M
 Keywords:

 Mathematics  Metric Geometry;
 Mathematics  Complex Variables;
 30L10
 EPrint:
 46 pages, 8 figures