@article{d1301ce0077a45f9a819acf9c1ce51a8,
title = "Carnot rectifiability of sub-Riemannian manifolds with constant tangent",
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.",
author = "{Le Donne}, Enrico and Robert Young",
note = "Funding Information: E.L.D. was partially supported by the Academy of Finland (grant 288501 “Geometry of subRiemannian groups” and by grant 322898 “Sub-Riemannian Geometry via Metric-geometry and Lie-group Theory”) and by the European Research Council (ERC Starting Grant 713998 GeoMeG “Geometry of Metric Groups”). R.Y. was supported by NSF grant 1612061. The authors wish to thank the anonymous referee and Gioacchino Antonelli for feedback on an earlier version of the paper which led to several improvements. Publisher Copyright: {\textcopyright} 2023 Scuola Normale Superiore. All rights reserved.",
year = "2023",
doi = "10.2422/2036-2145.201902_005",
language = "English (US)",
volume = "24",
pages = "71--96",
journal = "Annali della Scuola Normale Superiore di Pisa - Classe di Scienze",
issn = "0391-173X",
publisher = "Scuola Normale Superiore",
number = "1",
}