Geometrically finite groups, Patterson-Sullivan measures and Ratner's rigidity theorem
type: Item
instance of: scholarly article
title: Geometrically finite groups, Patterson-Sullivan measures and Ratner's rigidity theorem
zbMATH Open document ID: 0667.57014
DOI: 10.1007/BF01234433
published in: Inventiones Mathematicae
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143772
review text: 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.
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 57S30
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 22E40
zbMATH DE Number: 4092361
zbMATH Keywords: rigidity of the horospherical foliations of geometrically finite hyperbolic manifolds
zbMATH Keywords: Patterson-Sullivan measure
zbMATH Keywords: nonexistence of invariant measurable distributions on the boundary of hyperbolic space
zbMATH Keywords: frame flow
author: Livio Flaminio
author: Ralf Spatzier
MaRDI profile type: Publication
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Wikidata QID: Q125924547
OpenAlex ID: W2119461448
description: scientific article; zbMATH DE number 4092361