, Volume 320, Issue 1, pp 1-10

A Sard theorem for the distance function

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Abstract.

In this article, we prove that the set of all critical values of the distance function from a submanifold of a complete Riemannian manifold whose dimension is less than 5 is of Lebesgue measure zero.

Received November 26, 1999 / Published online April 12, 2001