scholarly journals Lipschitz and Bi-Lipschitz maps from PI spaces to Carnot groups

2020 ◽  
Vol 69 (5) ◽  
pp. 1685-1731
Author(s):  
Guy David ◽  
Kyle Kinneberg
Keyword(s):  
Carnot Groups ◽  
Lipschitz Maps

scholarly journals BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Sean Li
Keyword(s):  
Carnot Group ◽  
Carnot Groups ◽  
Lipschitz Maps ◽  
Lipschitz Map

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 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.

Extremals in some classes of Carnot groups

2011 ◽  
Vol 55 (3) ◽  
pp. 633-646 ◽  
Author(s):  
TiRen Huang ◽  
XiaoPing Yang
Keyword(s):  
Carnot Groups

scholarly journals On the gradient set of Lipschitz maps

2008 ◽  
Vol 2008 (625) ◽  
Author(s):  
Bernd Kirchheim ◽  
László Székelyhidi
Keyword(s):  
Lipschitz Maps

Singular integrals on C1,α regular curves in Carnot groups

2021 ◽  
Author(s):  
Vasileios Chousionis ◽  
Sean Li ◽  
Scott Zimmerman
Keyword(s):  
Singular Integrals ◽  
Carnot Groups
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