A1 Journal article (refereed)
Carnot rectifiability of sub-Riemannian manifolds with constant tangent (2023)

Le Donne, E., & Young, R. (2023). Carnot rectifiability of sub-Riemannian manifolds with constant tangent. Annali della Scuola Normale Superiore di Pisa: Classe di Scienze, 24(1), 71-96. https://doi.org/10.2422/2036-2145.201902_005

JYU authors or editors

Publication details

All authors or editors: Le Donne, Enrico; Young, Robert

Journal or series: Annali della Scuola Normale Superiore di Pisa: Classe di Scienze

ISSN: 0391-173X

eISSN: 2036-2145

Publication year: 2023

Publication date: 13/10/2021

Volume: 24

Issue number: 1

Pages range: 71-96

Publisher: Scuola Normale Superiore - Edizioni della Normale

Publication country: Italy

Publication language: English

DOI: https://doi.org/10.2422/2036-2145.201902_005

Publication open access: Not open

Publication channel open access: 

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1901.11227

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.

Keywords: differential geometry; Lie groups; manifolds (mathematics)

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Ministry reporting: Yes

Reporting Year: 2023

Preliminary JUFO rating: 2