Published June 2005
| Submitted
Journal Article
Open
Proximality and Equidistribution on the Furstenberg Boundary
- Creators
- Gorodnik, Alexander
- Maucourant, François
Chicago
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Abstract
Let G be a connected semisimple Lie group with finite center and without compact factors, P a minimal parabolic subgroup of G, and Γ a lattice in G. We prove that every Γ-orbits in the Furstenberg boundary G/P is equidistributed for the averages over Riemannian balls. The proof is based on the proximality of the action of Γ on G/P.
Additional Information
© Springer 2005. (Received: 21 September 2004; accepted in final form: 15 April 2005) Partially supported by NSF grant 0400631. The main ideas of this paper were developed during the workshop "Ergodic properties of geometric group actions" in Summer 2003. The authors would like to express deep appreciation to the organizers of this workshop and to the Max Planck Institute of Mathematics for its support. We also would like to thank R. Spatzier for raising the problem solved in this paper during the workshop and to E. Breuillard and Y. Guivarc'h for explaining the history of the subject.Attached Files
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Additional details
- Eprint ID
- 98169
- DOI
- 10.1007/s10711-005-5539-8
- Resolver ID
- CaltechAUTHORS:20190823-105107574
- NSF
- DMS-0400631
- Created
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2019-08-23Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field