Multiplicity and stability of closed geodesics on positively curved Finsler $4$-spheres

Huagui Duan, Dong Xie

In this paper, we prove that for every Finsler $4$-dimensional sphere $(S^4,F)$ with reversibility $\lambda$ and flag curvature $K$ satisfying $\frac{25}{9}\left(\fracλ{1+λ}\right)^2<K\l…