Quasisymmetric Koebe uniformization (Q373504)

Summary: 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.