Inventiones mathematicae

, Volume 99, Issue 1, pp 601–626

Geometrically finite groups, Patterson-Sullivan measures and Ratner's ridigity theorem

  • L. Flaminio
  • R. J. Spatzier


The rigidity properties of the horospherical foliations of geometrically finite hyperbolic manifolds are investigated. Ratner's theorem generalizes to these foliations with respect to the Patterson-Sullivan measure. In the spirit of Mostow, we prove the nonexistence of invariant measurable distributions on the boundary of hyperbolic space for geometrically finite groups. Finally, we show that the frame flow on geometrically finite hyperbolic manifolds is Bernoulli.


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • L. Flaminio
    • 1
  • R. J. Spatzier
    • 2
  1. 1.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Department of MathematicsSUNY at Stony BrookUSA

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