Mathematische Annalen

, Volume 320, Issue 1, pp 1–10 | Cite as

A Sard theorem for the distance function

  • Jin-ichi Itoh
  • Minoru Tanaka
Original articles


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.

Mathematics Subject Classification (1991): 53C22, 28A78 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jin-ichi Itoh
    • 1
  • Minoru Tanaka
    • 2
  1. 1.Faculty of Education, Kumamoto University, Kumamoto 860-8555, Japan (e-mail: JP
  2. 2.Department of Mathematics, Tokai University, Hiratsuka 259-1292, Japan (e-mail: JP

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