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arXiv · 1501.04610

BiLipschitz decomposition of Lipschitz maps between Carnot groups

Sean Li
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Abstract

Let $f : G \to H$ be a Lipschitz map between two Carnot groups. We show that if $B$ is ball of $G$, then there exists a subset $Z \subset B$, whose image in $H$ under $f$ has small Hausdorff content, such that $B \backslash Z$ can be decomposed into a controlled number of pieces, the restriction of $f$ on each of which is quantitatively biLipschitz. This extends a result of \cite{meyerson}, which proved the same result, but with the restriction that $G$ has an appropriate discretization. We provide an example of a Carnot group not admitting such a discretization.

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Sean Li. 2015-08-29. BiLipschitz decomposition of Lipschitz maps between Carnot groups. https://arxiv.org/abs/1501.04610

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