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.
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Sergei Merenkov, Kevin Wildrick, Quasisymmetric Koebe uniformization. Rev. Mat. Iberoam. 29 (2013), no. 3, pp. 859–910DOI 10.4171/RMI/743