manuscripta mathematica

, Volume 113, Issue 2, pp 251–265

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


DOI: 10.1007/s00229-003-0436-7

Cite this article as:
Rifford, L. manuscripta math. (2004) 113: 251. doi:10.1007/s00229-003-0436-7


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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Institut Girard DesarguesUniversité Claude Bernard Lyon IVilleurbanneFrance