Quasisymmetric Koebe Uniformization

Details Quasisymmetric Koebe Uniformization Quasisymmetric Koebe Uniformization

2011-09-15

arxiv.org/abs/1109.3441v1

Mathematics

Metric Geometry

46 pages, 8 figures

Scientific paper

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.

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