Quasisymmetric parametrizations of two-dimensional metric spheres

Details Quasisymmetric parametrizations of two-dimensional metric spheres Quasisymmetric parametrizations of two-dimensional metric spheres

2001-07-24

arxiv.org/abs/math/0107171v1

Mathematics

Metric Geometry

Scientific paper

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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