BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups

• Autorzy: Sean Li
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Carnot group; sub-riemannian geometry; Lipschitz maps

Kategorie tematyczne

• 28A78: Hausdorff and packing measures
• 53C17: Sub-Riemannian geometry

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-01-20

zaakceptowano

2015-07-08

online

2015-09-01

Twórcy

autor

Sean Li

• Department of Mathematics, The University of Chicago, Chicago, IL 60637

Bibliografia

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Identyfikatory

DOI

10.1515/agms-2015-0014