论文标题
在封闭的Finsler和Riemannian表面上等分分布封闭的大地测量学
Equidistributed Closed Geodesics on Closed Finsler and Riemannian Surfaces
论文作者
论文摘要
在本文中，我们在每个封闭的表面上都建立了一个非排定封闭的大地测量学序列的等分分配序列。证明依赖于Cristofaro-Gardiner，Hutchings和Ramos建立的嵌入式接触同源性的体积属性，以及特定的局部变异结构和横向论证。我们的方法是由IRIE的等均分配结果进行的，其中三维REEB流动以及Marques，Neves和Song [27]给出的类似结果，用于嵌入的最小超曲面。
In this paper, we establish the existence of an equidistributed sequence of nondegenerate closed geodesics for generic Finsler, symmetric Finsler and Riemannian metrics on every closed surface. The proof relies on the volume property of embedded contact homology, established by Cristofaro-Gardiner, Hutchings and Ramos, along with specific local variational constructions and transversality arguments. Our approach is motivated by Irie's equidistribution result in [19] for three-dimensional Reeb flows and the analogous result presented by Marques, Neves and Song [27] for embedded minimal hypersurfaces.
