Multiplicity of non-contractible closed geodesics on Finsler compact space forms

作者：Liu, Hui; Wang, Yuchen^*

来源：Calculus of Variations and Partial Differential Equations, 2022, 61(6): 224.

DOI：10.1007/s00526-022-02323-3

• FADELL-RABINOWITZ INDEX
• EXISTENCE
• RESONANCE

Let M = S-n/Gamma and h be a nontrivial element of finite order p in pi(1)(M), where the integer n, p >= 2, Gamma is a finite abelian group which acts freely and isometrically on the n-sphere and therefore M is diffeomorphic to a compact space form. In this paper, we prove that for every irreversible Finsler compact space form (M, F) with reversibility lambda and flag curvature K satisfying @@@ 4p(2)/(p+1)(2) (lambda/lambda+1)(2) < K <= 1, lambda < p+1/p-1, @@@ there exist at least n - 1 non-contractible closed geodesics of class [h]. In addition, if the metric F is bumpy and @@@ (4p/2p+1)(2) (lambda/lambda+1)(2) < K <= 1, lambda < 2p+1/2p-1, @@@ then there exist at least 2 [n+1/2] non-contractible closed geodesics of class [h], which is the optimal lower bound due to Katok's example. For C-4-generic Finsler metrics, there are infinitely many non-contractible closed geodesics of class [h] on (M, F) if lambda(2/)(lambda+1)(2) < K <= 1 with n being odd, or lambda(2)/(lambda+1)(2) 4/(n-1)(2) < K <= 1 with n being even.

• 单位
  武汉大学