Closed geodesics on reversible Finsler 2-spheres

Guido de Philippis (1) , Michele Marini (2) , Marco Mazzucchelli (1) , Stefan Suhr (3)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 SNS - Scuola Normale Superiore di Pisa
3 Fachbereich Mathematik [Hamburg]

We extend two celebrated theorems on closed geodesics of Riemannian 2-spheres to the larger class of reversible Finsler 2-spheres: Lusternik-Schnirelmann's theorem asserting the existence of three simple closed geodesics, and Bangert-Franks-Hingston's theorem asserting the existence of infinitely many closed geodesics. In order to prove the first theorem, we employ the generalization of Grayson's curve shortening flow developed by Angenent-Oaks.

Domaines: Géométrie différentielle [math.DG]; Systèmes dynamiques [math.DS]

Guido de Philippis, Michele Marini, Marco Mazzucchelli, Stefan Suhr. Closed geodesics on reversible Finsler 2-spheres. Journal of Fixed Point Theory and Applications, 2022, ⟨10.1007/s11784-022-00962-9⟩. ⟨hal-02467505⟩