We shall review recent results obtained in the study of some periodic variational problems on Riemannian and Lorentzian manifolds with boundary. Firstly we shall analyze the existence. of closed geodesics on a Riemannian manifold (M, < (.),(.)> (R))Then we shall deal respectively with periodic trajectories and periodic trajectories under a vectorial potential on stationary Lorentz manifolds. Finally, we discuss the different hypotheses on the boundary, and state some open questions.
|Titolo:||Remarks on some variational problems on non-complete manifolds|
|Data di pubblicazione:||2001|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1016/S0362-546X(01)00410-2|
|Appare nelle tipologie:||1.1 Articolo in rivista|