Abstract
CAT(−1) spaces are generalizations of manifolds with negative curvature. In this paper, we prove three types of rigidity results related to CAT(−1) spaces, namely the rigidity of the isometric actions on CAT(−1) spaces under the commensurability subgroups, the higher rank lattices and certain ergodic cocycles. The main idea for our approach relies on a study of the boundary theory we established for the general CAT(−1) spaces.
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Gao, Y. Superrigidity for homomorphisms into isometry groups of CAT(−1) spaces. Transformation Groups 2, 289–323 (1997). https://doi.org/10.1007/BF01234662
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DOI: https://doi.org/10.1007/BF01234662