Tukia's isomorphism theorem in CAT(-1) spaces

@article{Das2015TukiasIT,
  title={Tukia's isomorphism theorem in CAT(-1) spaces},
  author={Tushar Das and David Simmons and Mariusz Urba'nski},
  journal={arXiv: Dynamical Systems},
  year={2015}
}
We prove a generalization of Tukia's ('85) isomorphism theorem which states that isomorphisms between geometrically finite groups extend equivariantly to the boundary. Tukia worked in the setting of real hyperbolic spaces of finite dimension, and his theorem cannot be generalized as stated to the setting of CAT($-1$) spaces. We exhibit examples of type-preserving isomorphisms of geometrically finite subgroups of finite-dimensional rank one symmetric spaces of noncompact type (ROSSONCTs) whose… 

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Mostow type rigidity theorems
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