Subdifferentials and minimizing Sard conjecture in sub-Riemannian geometry

Ludovic Rifford

doi:10.5802/jep.242

Subdifferentials and minimizing Sard conjecture in sub-Riemannian geometry
[Sous-différentiels et conjecture de Sard minimisante en géométrie sous-riemannienne]

Ludovic Rifford ¹

¹ Université Côte d’Azur, CNRS, Labo. J.-A. Dieudonné, UMR CNRS 7351 Parc Valrose, 06108 Nice Cedex 02, France

Journal de l’École polytechnique — Mathématiques, Tome 10 (2023), pp. 1195-1244.

Résumé
Abstract

On utilise des techniques d’analyse non-lisse et de théorie géométrique de la mesure pour produire de nouveaux exemples de structures sous-riemanniennes complètes vérifiant la conjecture de Sard minimisante. On démontre en particulier que les structures sous-riemanniennes complètes associées à des distributions de co-rang $2$ ou génériques de rang $\geq 2$ vérifient la conjecture de Sard minimisante.

We use techniques from nonsmooth analysis and geometric measure theory to provide new examples of complete sub-Riemannian structures satisfying the Minimizing Sard conjecture. In particular, we show that complete sub-Riemannian structures associated with distributions of co-rank $2$ or generic distributions of rank $\geq 2$ satisfy the Minimizing Sard conjecture.

Reçu le : 2023-02-13
Accepté le : 2023-09-07
Publié le : 2023-09-14

DOI : 10.5802/jep.242

Classification : 53C17, 49J52
Keywords: Sub-Riemannian geometry, nonsmooth analysis, geometric measure theory
Mot clés : Géométrie sous-riemannienne, analyse non-lisse, théorie géométrique de la mesure

Affiliations des auteurs :

Ludovic Rifford ¹

¹ Université Côte d’Azur, CNRS, Labo. J.-A. Dieudonné, UMR CNRS 7351 Parc Valrose, 06108 Nice Cedex 02, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Subdifferentials and {minimizing~Sard~conjecture} in {sub-Riemannian~geometry}},
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Ludovic Rifford. Subdifferentials and minimizing Sard conjecture in sub-Riemannian geometry. Journal de l’École polytechnique — Mathématiques, Tome 10 (2023), pp. 1195-1244. doi : 10.5802/jep.242. https://jep.centre-mersenne.org/articles/10.5802/jep.242/

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