Quasisymmetric Koebe Uniformization

  title={Quasisymmetric Koebe Uniformization},
  author={Sergei Merenkov and Kevin Wildrick},
  journal={arXiv: Metric Geometry},
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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