JournalsrmiVol. 29, No. 3pp. 859–910

Quasisymmetric Koebe uniformization

  • Sergei Merenkov

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

    Universität Bern, Switzerland
Quasisymmetric Koebe uniformization cover
Download PDF

Abstract

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 XX homeomorphic to a domain in the standard 2-sphere S2\mathbb{S}^2 to be quasisymmetrically equivalent to a circle domain in S2\mathbb{S}^2. 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