Existence of closed geodesics on Finsler $n$-spheres

Wei Wang

In this paper, we prove that on every Finsler $n$-sphere $(S^n,F)$ with reversibility $\lambda$ satisfying $F^2<(\frac{\lambda +1}{\lambda }{)}^2{g}_0$ and $l(S^n,F)\ge \pi (1+\frac{1}{\lambda })$, there always exist…