Convexity of Domains of Riemannian Manifolds
Copyright policy )Convexity of Domains of Riemannian Manifolds
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.
20 pages, 2 figures
- Instituto Politécnico Nacional Mexico
- Polytechnic University of Bari Italy
- University of Bari Aldo Moro Italy
- University of Granada Spain
Mathematics - Differential Geometry, convexity, Riemannian manifold, Boundary, convexity, geodesic., 58E10, 53C22, 53C20, Dynamical Systems (math.DS), Geodesics in global differential geometry, Global Riemannian geometry, including pinching, boundary, trajectories of Lagrangian systems, Differential Geometry (math.DG), completeness, FOS: Mathematics, Mathematics - Dynamical Systems, geodesic, Variational problems in applications to the theory of geodesics (problems in one independent variable)
Mathematics - Differential Geometry, convexity, Riemannian manifold, Boundary, convexity, geodesic., 58E10, 53C22, 53C20, Dynamical Systems (math.DS), Geodesics in global differential geometry, Global Riemannian geometry, including pinching, boundary, trajectories of Lagrangian systems, Differential Geometry (math.DG), completeness, FOS: Mathematics, Mathematics - Dynamical Systems, geodesic, Variational problems in applications to the theory of geodesics (problems in one independent variable)
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