Closed geodesics on reversible Finsler 2-spheres

Guido De Philippis, Michele Marini, Marco Mazzucchelli, Stefan Suhr

Research output: Contribution to journalArticlepeer-review

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. To prove the first theorem, we employ the generalization of Grayson’s curve shortening flow developed by Angenent–Oaks.

Original languageEnglish (US)
Article number19
JournalJournal of Fixed Point Theory and Applications
Volume24
Issue number2
DOIs
StatePublished - Jun 2022

Keywords

  • Closed geodesics
  • curve shortening flow
  • Lusternik–Schnirelmann theory
  • reversible Finsler metrics

ASJC Scopus subject areas

  • Modeling and Simulation
  • Geometry and Topology
  • Applied Mathematics

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