A propos des sphères sous-riemanniennes

Nous démontrons qu’en l’absence de courbe minimisante singulilère, la fonction distance sous-riemannienne, localement lipschitzienne hors de la diagonale, vérifie un théorème de Sard. On en déduit que les sphères sous-riemanniennes sont des hypersurfaces lipschitziennes pour presque tout rayon dans dSR(q0, Q). Abstract. We prove that, in absence of singular minimizing curve, the sub-riemannian distance function is locally Lipschitz outside the diagonal and satisfies Sard’s theorem. Hence we deduce that the spheres are Lipschitz hypersurfaces for almost every radius in dSR(q0, Q). We prove that, in absence of singular minimizing curve, the sub-riemannian distance function is locally Lipschitz outside the diagonal and satisfies Sard’s theorem. Hence we deduce that the spheres are Lipschitz hypersurfaces for almost every radius in dSR(q0, Q).