A Morse-Sard theorem for the distance function on Riemannian manifolds

Ludovic Rifford (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

We prove that the set of critical values of the distance function from a submanifold of a complete Riemannian manifold is of Lebesgue measure zero. In this way, we extend a result of Itoh and Tanaka.

Domaines: Mathématiques générales [math.GM]; Géométrie différentielle [math.DG]

Ludovic Rifford. A Morse-Sard theorem for the distance function on Riemannian manifolds. Manuscripta mathematica, 2004, 113 (2), pp.251-265. ⟨hal-00769005⟩