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Proximality and Equidistribution on the Furstenberg Boundary

Gorodnik, Alexander and Maucourant, François (2005) Proximality and Equidistribution on the Furstenberg Boundary. Geometriae Dedicata, 113 (1). pp. 197-213. ISSN 0046-5755. doi:10.1007/s10711-005-5539-8. https://resolver.caltech.edu/CaltechAUTHORS:20190823-105107574

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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.


Item Type:Article
Related URLs:
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https://doi.org/10.1007/s10711-005-5539-8DOIArticle
https://rdcu.be/bPnAYPublisherFree ReadCube access
https://arxiv.org/abs/math/0406219arXivDiscussion Paper
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.
Funders:
Funding AgencyGrant Number
NSFDMS-0400631
Subject Keywords:equidistribution, proximality, Furstenberg boundary, lattices, Lie groups
Issue or Number:1
Classification Code:Mathematics Subject Classifications (2000). 37B05, 22E40.
DOI:10.1007/s10711-005-5539-8
Record Number:CaltechAUTHORS:20190823-105107574
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190823-105107574
Official Citation:Gorodnik, A. & Maucourant, F. Geom Dedicata (2005) 113: 197. https://doi.org/10.1007/s10711-005-5539-8
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98169
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:23 Aug 2019 18:14
Last Modified:16 Nov 2021 17:37

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