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Lipschitz and bi-Lipschitz maps from PI spaces to Carnot groups. (arXiv:1711.03533v1 [math.MG])
来源于:arXiv
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 Euclidean. For general Carnot
targets, we show that the existence of a bi-Lipschitz decomposition is
equivalent to a condition on the geometry of the image set. 查看全文>>