Quasisymmetric Koebe uniformization

  • Sergei Merenkov

    University of Illinois at Urbana-Champaign, USA
  • Kevin Wildrick

    Universität Bern, Switzerland


We study a quasisymmetric version of the classical Koebe uniformization theorem in the context of Ahlfors regular metric surfaces. We provide sufficient conditions for an Ahlfors 2-regular metric space homeomorphic to a domain in the standard 2-sphere to be quasisymmetrically equivalent to a circle domain in . We also give an example showing the sharpness of these conditions.

Cite this article

Sergei Merenkov, Kevin Wildrick, Quasisymmetric Koebe uniformization. Rev. Mat. Iberoam. 29 (2013), no. 3, pp. 859–910

DOI 10.4171/RMI/743