The existence of two closed geodesics on every Finsler 2-sphere

TL;DR

This paper proves that every Finsler 2-sphere has at least two distinct prime closed geodesics, solving a long-standing open problem in differential geometry.

Contribution

It establishes the existence of at least two closed geodesics on any Finsler 2-sphere, confirming a conjecture posed by Anosov in 1974.

Findings

At least two distinct prime closed geodesics exist on every Finsler 2-sphere

Solves the open problem posed by D. V. Anosov in 1974

Advances understanding of geodesic structures on Finsler manifolds

Abstract

In this paper, we prove that for every Finsler metric on the 2-dimensional sphere there exist at least two distinct prime closed geodesics. For the case of the two-sphere, this solves an open problem posed by D. V. Anosov in 1974.