Quasisymmetric parametrizations of two-dimensional metric spheres
Abstract
We study metric spaces homeomorphic to the 2-sphere, and find conditions under which they are quasisymmetrically homeomorphic to the standard 2-sphere. As an application of our main theorem we show that an Ahlfors 2-regular, linearly locally contractible metric 2-sphere is quasisymmetrically homeomorphic to the standard 2-sphere, answering a question of Heinonen and Semmes.
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