Convexity of Domains of Riemannian Manifolds

Authors: Bartolo R.¹; Germinario A.¹; Sánchez M.²

Source: Annals of Global Analysis and Geometry, Volume 21, Number 1, March 2002 , pp. 63-84(21)

Publisher: Springer

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Abstract:

In this paper the problem of the geodesic connectedness and convexity of incomplete Riemannian manifolds is analyzed. To this aim, a detailed study of the notion of convexity for the associated Cauchy boundary is carried out. In particular, under widely discussed hypotheses, we prove the convexity of open domains (whose boundaries may be nondifferentiable) of a complete Riemannian manifold. Variational methods are mainly used. Examples and applications are provided, including a result for dynamical systems on the existence of trajectories with fixed energy.

Keywords: boundary; convexity; geodesic

Language: English

Document Type: Regular paper

Affiliations: 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

Publication date: 2002-03-01