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Ergodicity of unipotent flows and Kleinian groups


Authors: Amir Mohammadi and Hee Oh
Journal: J. Amer. Math. Soc. 28 (2015), 531-577
MSC (2010): Primary 11N45, 37F35, 22E40; Secondary 37A17, 20F67
DOI: https://doi.org/10.1090/S0894-0347-2014-00811-0
Published electronically: June 4, 2014
MathSciNet review: 3300701
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Abstract: Let $ \mathcal {M}$ be a non-elementary convex cocompact hyperbolic $ 3$-manifold and $ \delta $ be the critical exponent of its fundamental group. We prove that a one-dimensional unipotent flow for the frame bundle of $ \mathcal {M}$ is ergodic for the Burger-Roblin measure if and only if $ \delta >1$.


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Additional Information

Amir Mohammadi
Affiliation: Department of Mathematics, The University of Texas at Austin, Austin, Texas 78750
Email: amir@math.utexas.edu

Hee Oh
Affiliation: Department of Mathematics, Yale University, New Haven, Connecticut 06520 and Korea Institute for Advanced Study, Seoul, Korea
Email: hee.oh@yale.edu

DOI: https://doi.org/10.1090/S0894-0347-2014-00811-0
Keywords: Geometrically finite hyperbolic groups, Ergodicity, Burger-Roblin measure, Bowen-Margulis-Sullivan measure
Received by editor(s): September 15, 2012
Received by editor(s) in revised form: February 23, 2014
Published electronically: June 4, 2014
Additional Notes: The first author was supported in part by NSF Grant #1200388.
The second author was supported in part by NSF Grant #1068094.
Article copyright: © Copyright 2014 American Mathematical Society

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