Transitive bilipschitz group actions and bilipschitz parametrizations
David Freeman
30C6222E2551F99bilipschitz homogeneitymetric inversion
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.
Indiana University Mathematics Journal
2013
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10.1512/iumj.2013.62.4872
10.1512/iumj.2013.62.4872
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Indiana Univ. Math. J. 62 (2013) 311 - 331
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