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
Article

Summary

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations