Transitive bi-Lipschitz group actions and bi-Lipschitz parameterizations
Metric Geometry
2022-07-11 v3
Abstract
We prove that Ahlfors 2-regular quasisymmetric images of the Euclidean plane are bi-Lipschitz images of the plane 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.
Keywords
Cite
@article{arxiv.1203.4535,
title = {Transitive bi-Lipschitz group actions and bi-Lipschitz parameterizations},
author = {David M. Freeman},
journal= {arXiv preprint arXiv:1203.4535},
year = {2022}
}
Comments
Added an attribution and additional references prior to the proof of Theorem 2.2