Quasisymmetric parametrizations of two-dimensional metric spheres
Metric Geometry
2015-06-26 v1 Group Theory
Geometric Topology
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.
Keywords
Cite
@article{arxiv.math/0107171,
title = {Quasisymmetric parametrizations of two-dimensional metric spheres},
author = {Mario Bonk and Bruce Kleiner},
journal= {arXiv preprint arXiv:math/0107171},
year = {2015}
}