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Carnot rectifiability of sub-Riemannian manifolds with constant tangent. (arXiv:1901.11227v1 [math.MG])

来源于:arXiv
We show that if $M$ is a sub-Riemannian manifold and $N$ is a Carnot group such that the nilpotentization of $M$ at almost every point is isomorphic to $N$, then there are subsets of $N$ of positive measure that embed into $M$ by bilipschitz maps. Furthermore, $M$ is countably $N$--rectifiable, i.e., all of $M$ except for a null set can be covered by countably many such maps. 查看全文>>