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
Mots-clés : Geodesics, minimax problems, Finsler geometry
@article{COCV_2016__22_4_1282_0, author = {Michelat, Alexis and Rivi\`ere, Tristan}, title = {A {Viscosity} method for the min-max construction of closed geodesics}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1282--1324}, publisher = {EDP-Sciences}, volume = {22}, number = {4}, year = {2016}, doi = {10.1051/cocv/2016039}, zbl = {1353.49006}, language = {en}, url = {https://www.numdam.org/articles/10.1051/cocv/2016039/} }
TY - JOUR AU - Michelat, Alexis AU - Rivière, Tristan TI - A Viscosity method for the min-max construction of closed geodesics JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 1282 EP - 1324 VL - 22 IS - 4 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2016039/ DO - 10.1051/cocv/2016039 LA - en ID - COCV_2016__22_4_1282_0 ER -
%0 Journal Article %A Michelat, Alexis %A Rivière, Tristan %T A Viscosity method for the min-max construction of closed geodesics %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 1282-1324 %V 22 %N 4 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2016039/ %R 10.1051/cocv/2016039 %G en %F COCV_2016__22_4_1282_0
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. https://www.numdam.org/articles/10.1051/cocv/2016039/
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