Closed geodesics on reversible Finsler 2-spheres

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

Research output: Contribution to journalArticlepeer-review


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
Issue number2
StatePublished - Jun 2022


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

ASJC Scopus subject areas

  • Modeling and Simulation
  • Geometry and Topology
  • Applied Mathematics


Dive into the research topics of 'Closed geodesics on reversible Finsler 2-spheres'. Together they form a unique fingerprint.

Cite this