IUMJ

Title: Transitive bilipschitz group actions and bilipschitz parametrizations

Authors: David Freeman

Issue: Volume 62 (2013), Issue 1, 311-331

Abstract:

We prove that Ahlfors $2$-regular quasisymmetric images of $\mathbb{R}^2$ are bi-Lipschitz images of $\mathbb{R}^2$ if and only if they are uniformly bi-Lipschitz homogeneous with respect to a group. We also prove that certain geodesic spaces are bi-Lipschitz images of Carnot groups if they are inversion-invariant bi-Lipschitz homogeneous with respect to a group.