BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups

Sean Li

Analysis and Geometry in Metric Spaces (2015)

  • Volume: 3, Issue: 1, page 231-243, electronic only
  • ISSN: 2299-3274

Abstract

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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 BZcan 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.

How to cite

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Sean Li. "BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups." Analysis and Geometry in Metric Spaces 3.1 (2015): 231-243, electronic only. <http://eudml.org/doc/271760>.

@article{SeanLi2015,
abstract = {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 BZcan 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.},
author = {Sean Li},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Carnot group; sub-riemannian geometry; Lipschitz maps; bi-Lipschitz decomposition; homogeneous norm; Carnot-Carathéodory metrics; Hausdorff dimension; discretizability},
language = {eng},
number = {1},
pages = {231-243, electronic only},
title = {BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups},
url = {http://eudml.org/doc/271760},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Sean Li
TI - BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups
JO - Analysis and Geometry in Metric Spaces
PY - 2015
VL - 3
IS - 1
SP - 231
EP - 243, electronic only
AB - 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 BZcan 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.
LA - eng
KW - Carnot group; sub-riemannian geometry; Lipschitz maps; bi-Lipschitz decomposition; homogeneous norm; Carnot-Carathéodory metrics; Hausdorff dimension; discretizability
UR - http://eudml.org/doc/271760
ER -

References

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