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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Ergodicity of unipotent flows and Kleinian groups
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by Amir Mohammadi and Hee Oh PDF
J. Amer. Math. Soc. 28 (2015), 531-577 Request permission

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
  • MR Author ID: 886399
  • 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
  • MR Author ID: 615083
  • Email: hee.oh@yale.edu
  • 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.
  • © Copyright 2014 American Mathematical Society
  • 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
  • MathSciNet review: 3300701