BiLipschitz decomposition of Lipschitz maps between Carnot groups

2015/01/19 by Li, Sean
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1501.04610

Abstract

Let f : G → H be a Lipschitz map between two Carnot groups. We show that if B is ball of G, then there exists a subset Z ⊂ 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 \citemeyerson, 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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