Geodesic
BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups
Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1.

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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.
Mots-clés : Carnot group, sub-riemannian geometry, Lipschitz maps 
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     author = {Li, Sean},
     title = {BiLipschitz {Decomposition} of {Lipschitz} {Maps} between {Carnot} {Groups}},
     journal = {Analysis and Geometry in Metric Spaces},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {2015},
     zbl = {1331.53055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a3/}
}
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Li, Sean. BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups. Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a3/