On the rigidity of discrete isometry groups of negatively curved spaces

@article{Hersonsky1997OnTR,
  title={On the rigidity of discrete isometry groups of negatively curved spaces},
  author={Sa'ar Hersonsky and F. Paulin},
  journal={Commentarii Mathematici Helvetici},
  year={1997},
  volume={72},
  pages={349-388}
}
Abstract. We prove an ergodic rigidity theorem for discrete isometry groups of CAT(-1) spaces. We give explicit examples of divergence isometry groups with infinite covolume in the case of trees, piecewise hyperbolic 2-polyhedra, hyperbolic Bruhat-Tits buildings and rank one symmetric spaces. We prove that two negatively curved Riemannian metrics, with conical singularities of angles at least $ 2\pi $, on a closed surface, with boundary map absolutely continuous with respect to the Patterson… Expand

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