Geometrically finite groups, Patterson-Sullivan measures and Ratner's rigidity theorem
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.
rigidity of the horospherical foliations of geometrically finite hyperbolic manifolds
nonexistence of invariant measurable distributions on the boundary of hyperbolic space
scientific article; zbMATH DE number 4092361
scientific article