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

  title={Lipschitz and Bi-Lipschitz maps from PI spaces to Carnot groups},
  author={Guy C. David and Kyle Kinneberg},
  journal={Indiana University Mathematics Journal},
This paper deals with the problem of finding bi-Lipschitz behavior in non-degenerate Lipschitz maps between metric measure spaces. Specifically, we study maps from (subsets of) Ahlfors regular PI spaces into sub-Riemannian Carnot groups. We prove that such maps have many bi-Lipschitz tangents, verifying a conjecture of Semmes. As a stronger conclusion, one would like to know whether such maps decompose into countably many bi-Lipschitz pieces. We show that this is true when the Carnot group is… 
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