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

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Abstract

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.

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  1. Institut Girard Desargues, Université Claude Bernard Lyon I, 21 avenue Claude Bernard, 69622, Villeurbanne, France

    Ludovic Rifford

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  1. Ludovic Rifford
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Correspondence to Ludovic Rifford.

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Mathematics Subject Classification (2000): 53C22, 28A78, 49J52

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Rifford, L. A Morse-Sard theorem for the distance function on Riemannian manifolds. manuscripta math. 113, 251–265 (2004). https://doi.org/10.1007/s00229-003-0436-7

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  • DOI: https://doi.org/10.1007/s00229-003-0436-7

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