Convexity of Domains of Riemannian Manifolds |
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Authors: | Rossella Bartolo Anna Germinario Miguel Sánchez |
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Institution: | (1) Dipartimento Interuniversitario di Matematica, Politecnico di Bari, via E. Orabona, 4, 70125 Bari, Italy;(2) Departamento de Geometría y Topología, Fac. Ciencias, Univ. Granada, Avenida Fuentenueva s/n, 18071 Granada, Spain |
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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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Keywords: | boundary convexity geodesic |
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