A Viscosity method for the min-max construction of closed geodesics
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1282-1324.

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 ε-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.

DOI : 10.1051/cocv/2016039
Classification : 49J35, 58B20, 58E10
Mots clés : Geodesics, minimax problems, Finsler geometry
Michelat, Alexis 1 ; Rivière, Tristan 1

1 Department of Mathematics, ETH Zentrum, 8093 Zürich, Switzerland.
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Michelat, Alexis; Rivière, Tristan. A Viscosity method for the min-max construction of closed geodesics. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1282-1324. doi : 10.1051/cocv/2016039. http://archive.numdam.org/articles/10.1051/cocv/2016039/

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