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Convexity of Domains of Riemannian Manifolds

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Abstract

In this paper the problem of the geodesic connectedness and convexity ofincomplete Riemannian manifolds is analyzed. To this aim, a detailedstudy of the notion of convexity for the associated Cauchy boundary iscarried out. In particular, under widely discussed hypotheses,we prove the convexity of open domains (whose boundaries may benondifferentiable) of a complete Riemannian manifold. Variationalmethods are mainly used. Examples and applications are provided,including a result for dynamical systems on the existence oftrajectories with fixed energy.

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Authors and Affiliations

  1. Dipartimento Interuniversitario di Matematica, Politecnico di Bari, via E. Orabona, 4, 70125, Bari, Italy

    Rossella Bartolo & Anna Germinario

  2. Departamento de Geometría y Topología, Fac. Ciencias, Univ. Granada, Avenida Fuentenueva s/n, 18071, Granada, Spain

    Miguel Sánchez

Authors
  1. Rossella Bartolo
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  2. Anna Germinario
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  3. Miguel Sánchez
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Bartolo, R., Germinario, A. & Sánchez, M. Convexity of Domains of Riemannian Manifolds. Annals of Global Analysis and Geometry 21, 63–84 (2002). https://doi.org/10.1023/A:1014231603588

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  • DOI: https://doi.org/10.1023/A:1014231603588

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