A Viscosity method for the min-max construction of closed geodesics

Autor: Alexis Michelat, Tristan Rivière
Rok vydání: 2016
Předmět:
Zdroj: ESAIM: Control, Optimisation and Calculus of Variations. 22:1282-1324
ISSN: 1262-3377
1292-8119
DOI: 10.1051/cocv/2016039
Popis: We present a viscosity approach to the min-max construction of closed geodesics on compact Riemannian manifolds of arbitrary dimension. The existence is proved in the case of surfaces, and reduced to a topological condition in general. We also construct counter-examples in dimension 1 and 2 to the e -regularity in the convergence procedure. Furthermore, we prove the lower semi-continuity of the index of our sequence of critical points converging towards a closed non-trivial geodesic.
Databáze: OpenAIRE