# BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups

Analysis and Geometry in Metric Spaces (2015)

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

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topSean 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 -

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