Closed geodesics on reversible Finsler 2-spheres
Differential Geometry
2022-04-11 v2 Dynamical Systems
Symplectic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.2002.00415,
title = {Closed geodesics on reversible Finsler 2-spheres},
author = {Guido De Philippis and Michele Marini and Marco Mazzucchelli and Stefan Suhr},
journal= {arXiv preprint arXiv:2002.00415},
year = {2022}
}
Comments
57 pages, 4 figures; final version: a few corrections to Theorem 1.2, to Sections 2.5-6, and to Section 5.4