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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.

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Authors and Affiliations

  1. Faculty of Education, Kumamoto University, Kumamoto 860-8555, Japan (e-mail: j-itoh@gpo.kumamoto-u.ac.jp) , , , , , , JP

    Jin-ichi Itoh

  2. Department of Mathematics, Tokai University, Hiratsuka 259-1292, Japan (e-mail: m-tanaka@sm.u-tokai.ac.jp) , , , , , , JP

    Minoru Tanaka

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  1. Jin-ichi Itoh
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  2. Minoru Tanaka
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Received November 26, 1999 / Published online April 12, 2001

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Itoh, Ji., Tanaka, M. A Sard theorem for the distance function. Math Ann 320, 1–10 (2001). https://doi.org/10.1007/PL00004462

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  • DOI: https://doi.org/10.1007/PL00004462

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