Transitive bi-Lipschitz group actions and bi-Lipschitz parameterizations

2012/03/20 by David Freeman, Freeman, David M.
Mathematics · #Morphological variations and asymmetry #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1203.4535

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.

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