Uniformization of two-dimensional metric surfaces (Q517435)

The author studies metric spaces that are homeomorphic to the Euclidean plane or sphere and have locally finite Hausdorff 2-measure. The main result gives a necessary and sufficient condition for such spaces to be QC equivalent to the Euclidean plane, disk, or sphere. This result gives a new approach to the Bonk-Kleiner theorem on parametrizations of Ahlfors 2-regular spheres by quasisymmetric maps.