Calculus of Variations and Geometric Measure Theory

G. De Philippis - M. Marini - M. Mazzucchelli - S. Suhr

Closed geodesics on reversible Finsler 2-spheres

created by mazzucchelli on 03 Feb 2020
modified on 04 Feb 2020



Inserted: 3 feb 2020
Last Updated: 4 feb 2020

Year: 2020

ArXiv: 2002.00415 PDF


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.