SHARP REGULARITY OF SUB-RIEMANNIAN LENGTH-MINIMIZING CURVES
Résumé
A longstanding open question in sub-Riemannian geometry is the smoothness of (the arc-length parameterization of) length-minimizing curves. In [19], this question is negative answered, with an example of a C 2 but not C 3 length-minimizer of a real-analytic (even polynomial) sub-Riemannian structure. In this paper, we study a class of examples of sub-Riemannian structures that generalizes that presented in [19], and we prove that length-minimizing curves must be at least of class C 2 within these examples. In particular, we prove that Theorem 1.1 in [19] is sharp. Contents 1. Introduction 1 2. Sub-Riemannian structures on R 3 4 3. Proof of Theorem 1.2 10 References 15
Domaines
Mathématiques [math]Origine | Fichiers produits par l'(les) auteur(s) |
---|