## 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 $\delta >1$.## References

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## Bibliographic 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