Remarks on some variational problems on non-complete manifolds

Authors
Bartolo, R Sanchez, M
Citation
R. Bartolo et M. Sanchez, Remarks on some variational problems on non-complete manifolds, NONLIN ANAL, 47(4), 2001, pp. 2887-2892
Citations number
11
Categorie Soggetti
Mathematics
Journal title
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
ISSN journal
0362546X → ACNP
Volume
47
Issue
4
Year of publication
2001
Pages
2887 - 2892
Database
ISI
SICI code
0362-546X(200108)47:4<2887:ROSVPO>2.0.ZU;2-M
Abstract
We shall review recent results obtained in the study of some periodic varia tional problems on Riemannian and Lorentzian manifolds with boundary. First ly we shall analyze the existence. of closed geodesics on a Riemannian mani fold (M, < (.),(.)> (R))Then we shall deal respectively with periodic traje ctories and periodic trajectories under a vectorial potential on stationary Lorentz manifolds. Finally, we discuss the different hypotheses on the bou ndary, and state some open questions.