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arXiv · 1901.11227

Carnot rectifiability of sub-Riemannian manifolds with constant tangent

Enrico Le Donne·Robert Young
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Abstract

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.

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Enrico Le Donne, Robert Young. 2019-01-31. Carnot rectifiability of sub-Riemannian manifolds with constant tangent. https://arxiv.org/abs/1901.11227

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