Subdifferentials and minimizing Sard conjecture in sub-Riemannian geometry
Journal de l’École polytechnique — Mathématiques, Volume 10 (2023), pp. 1195-1244.

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 2 satisfy the Minimizing Sard conjecture.

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 2 vérifient la conjecture de Sard minimisante.

Received:
Accepted:
Published online:
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

Ludovic Rifford 1

1 Université Côte d’Azur, CNRS, Labo. J.-A. Dieudonné, UMR CNRS 7351 Parc Valrose, 06108 Nice Cedex 02, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Ludovic Rifford. Subdifferentials and minimizing Sard conjecture in sub-Riemannian geometry. Journal de l’École polytechnique — Mathématiques, Volume 10 (2023), pp. 1195-1244. doi : 10.5802/jep.242. https://jep.centre-mersenne.org/articles/10.5802/jep.242/

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