Calculus of Variations and Geometric Measure Theory

E. Le Donne - R. Young

Carnot rectifiability of sub-Riemannian manifolds with constant tangent

created by ledonne on 12 Oct 2019
modified on 01 Dec 2019



Inserted: 12 oct 2019
Last Updated: 1 dec 2019

Year: 2019

ArXiv: 1901.11227 PDF


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.

Tags: GeoMeG