Pré-Publication, Document De Travail Année : 2025

SHARP REGULARITY OF SUB-RIEMANNIAN LENGTH-MINIMIZING CURVES

Alessandro Socionovo

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

Fichier principal
Vignette du fichier
Socionovo_Sharp_regularity_SR_length-minimizing_curves.pdf (524.26 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04886086 , version 1 (14-01-2025)

Identifiants

  • HAL Id : hal-04886086 , version 1

Citer

Alessandro Socionovo. SHARP REGULARITY OF SUB-RIEMANNIAN LENGTH-MINIMIZING CURVES. 2025. ⟨hal-04886086⟩
0 Consultations
0 Téléchargements

Partager

More