Applied Mathematics & Optimization

, Volume 47, Issue 1, pp 1–25

Hamilton—Jacobi Equations and Distance Functions on Riemannian Manifolds


  •  Mantegazza
    • Scuola Normale Superiore, Pisa 56126, Italy,,
  •  Mennucci
    • Scuola Normale Superiore, Pisa 56126, Italy,,

DOI: 10.1007/s00245-002-0736-4

Cite this article as:
Mantegazza & Mennucci Appl Math Optim (2002) 47: 1. doi:10.1007/s00245-002-0736-4

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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© 2002 Springer-Verlag New York Inc.