Convexity of domains of Riemannian manifolds

Details Convexity of domains of Riemannian manifolds Convexity of domains of Riemannian manifolds

2000-04-12

arxiv.org/abs/math/0004075v1

Mathematics

Differential Geometry

20 pages, 2 figures

Scientific paper

In this paper we analyze the problem of the geodesic connectedness of subsets of Riemannian manifolds. By using variational methods, the geodesic connectedness of open domains (whose boundaries can be not differentiable and not convex) of a smooth Riemannian manifold is proved. In some cases also the convexity of the domain is obtained. Moreover we present examples of the applicability and of the independence of the assumptions. Finally we give an application to the existence of trajectories with fixed energy of dynamical systems.

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