Applied Mathematics & Optimization

, Volume 47, Issue 1, pp 1-25

First online:

Hamilton—Jacobi Equations and Distance Functions on Riemannian Manifolds

  •  MantegazzaAffiliated withScuola Normale Superiore, Pisa 56126, Italy mantegaz@sns.it, mennucci@sns.it,
  • ,  MennucciAffiliated withScuola Normale Superiore, Pisa 56126, Italy mantegaz@sns.it, mennucci@sns.it,

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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.