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BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups

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Li S.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

Let f : G → H be a Lipschitz map between two Carnot groups. We show that if B is a ball of G, then there exists a subset Z ⊂ B, whose image in H under f has small Hausdorff content, such that B\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 [14], 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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1 Analysis and Geometry in Metric Spaces

1 Li S.

1 2015

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BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups