Ergodicity of unipotent flows and Kleinian groups

Mohammadi, Amir ¹   ; Oh, Hee ²

¹ Department of Mathematics, The University of Texas at Austin, Austin, Texas 78750
² Department of Mathematics, Yale University, New Haven, Connecticut 06520 and Korea Institute for Advanced Study, Seoul, Korea

Journal of the American Mathematical Society, Tome 28 (2015) no. 2, pp. 531-577

Résumé

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 $\delta >1$.

Détail

DOI : 10.1090/S0894-0347-2014-00811-0

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