Applied Mathematics & Optimization

, Volume 47, Issue 1, pp 1–25

Hamilton—Jacobi Equations and Distance Functions on Riemannian Manifolds

  •  Mantegazza
  •  Mennucci

Abstract. The paper is concerned with the properties of the distance function from a closed subset of a Riemannian manifold, with particular attention to the set of singularities.

Key words. Geodesic, Cut locus, Hamilton—Jacobi equation, Viscosity solution, Semiconcavity. AMS Classification. Primary 49F25, Secondary 53C22. 

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Copyright information

© 2002 Springer-Verlag New York Inc.

Authors and Affiliations

  •  Mantegazza
    • 1
  •  Mennucci
    • 1
  1. 1.Scuola Normale Superiore, Pisa 56126, Italy mantegaz@sns.it, mennucci@sns.it, IT

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