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 or generic distributions of rank 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 ou génériques de rang vérifient la conjecture de Sard minimisante.
Accepted:
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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
@article{JEP_2023__10__1195_0, author = {Ludovic Rifford}, title = {Subdifferentials and {minimizing~Sard~conjecture} in {sub-Riemannian~geometry}}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {1195--1244}, publisher = {\'Ecole polytechnique}, volume = {10}, year = {2023}, doi = {10.5802/jep.242}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.242/} }
TY - JOUR AU - Ludovic Rifford TI - Subdifferentials and minimizing Sard conjecture in sub-Riemannian geometry JO - Journal de l’École polytechnique — Mathématiques PY - 2023 SP - 1195 EP - 1244 VL - 10 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.242/ DO - 10.5802/jep.242 LA - en ID - JEP_2023__10__1195_0 ER -
%0 Journal Article %A Ludovic Rifford %T Subdifferentials and minimizing Sard conjecture in sub-Riemannian geometry %J Journal de l’École polytechnique — Mathématiques %D 2023 %P 1195-1244 %V 10 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.242/ %R 10.5802/jep.242 %G en %F JEP_2023__10__1195_0
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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