全局双曲极大紧AdS三维流形中闭测地线的计数
Counting closed geodesics in globally hyperbolic maximal compact AdS 3-manifolds
摘要：
给出了全局双曲极大紧Anti-De Sitter流形中闭测地线长度的定义。然后，我们证明了长度小于$R$的闭测地线的数量随着$R$指数快速增长，并且指数增长性与来自Mess参数化的两个双曲曲面的临界指数有关。我们得到了GHMC下拟Fuchsian流形的三个结果的等价结果：R。临界指数的Bowen刚性定理，A. Sanders隔离定理和C. McMullen的例子减轻了这个指数的行为时，表面范围超过Teichmüller空间。
英文摘要：
We propose a definition for the length of closed geodesics in a globally hyperbolic maximal compact (GHMC) Anti-De Sitter manifold. We then prove that the number of closed geodesics of length less than $R$ grows exponentially fast with $R$ and the exponential growth rate is related to the critical exponent associated to the two hyperbolic surfaces coming from Mess parametrization. We get an equivalent of three results for quasi-Fuchsian manifolds in the GHMC setting : R. Bowen's rigidity theorem of critical exponent, A. Sanders' isolation theorem and C. McMullen's examples lightening the behaviour of this exponent when the surfaces range over Teichmüller space.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
