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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access September 1, 2015

BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups

  • Sean Li


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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Received: 2015-1-20
Accepted: 2015-7-8
Published Online: 2015-9-1

© 2015 Sean Li

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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