Transitive bi-Lipschitz group actions and bi-Lipschitz parameterizations

Mathematics – Metric Geometry

Scientific paper

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To appear in the Indiana University Mathematics Journal

Scientific paper

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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