Ergodicity of unipotent flows and Kleinian groups

Mohammadi, Amir; Oh, Hee

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

Ergodicity of unipotent flows and Kleinian groups
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by Amir Mohammadi and Hee Oh

J. Amer. Math. Soc. 28 (2015), 531-577

DOI: https://doi.org/10.1090/S0894-0347-2014-00811-0

Published electronically: June 4, 2014

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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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