Revista Matemática Iberoamericana

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Volume 29, Issue 3, 2013, pp. 859–910
DOI: 10.4171/RMI/743

Published online: 2013-08-04

Quasisymmetric Koebe uniformization

Sergei Merenkov[1] and Kevin Wildrick

(1) University of Illinois at Urbana-Champaign, USA

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 $X$ homeomorphic to a domain in the standard 2-sphere $\mathbb{S}^2$ to be quasisymmetrically equivalent to a circle domain in $\mathbb{S}^2$. We also give an example showing the sharpness of these conditions.

Keywords: Quasiconformal mapping, metric spaces, uniformization

Merenkov Sergei, Wildrick Kevin: Quasisymmetric Koebe uniformization. Rev. Mat. Iberoamericana 29 (2013), 859-910. doi: 10.4171/RMI/743