Counting closed geodesics in globally hyperbolic maximal compact AdS 3-manifolds

@article{Glorieux2015CountingCG,
  title={Counting closed geodesics in globally hyperbolic maximal compact AdS 3-manifolds},
  author={Olivier Glorieux},
  journal={Geometriae Dedicata},
  year={2015},
  volume={188},
  pages={63-101}
}
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: Bowen’s rigidity theorem of… 
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