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Invariant Radon measures for Unipotent flows and products of Kleinian groups


Authors: Amir Mohammadi and Hee Oh
Journal: Proc. Amer. Math. Soc. 146 (2018), 1469-1479
MSC (2010): Primary 11N45, 37F35, 22E40; Secondary 37A17, 20F67
DOI: https://doi.org/10.1090/proc/13840
Published electronically: November 10, 2017
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Abstract: Let $ G= {\rm PSL}_2(\mathbb{F})$ where $ \mathbb{F}= \mathbb{R} , \mathbb{C}$, and consider the space $ Z=(\Gamma _1 \times \Gamma _2)\backslash (G\times G)$ where $ \Gamma _1<G$ is a co-compact lattice and $ \Gamma _2<G$ is a geometrically finite discrete Zariski dense subgroup. For a horospherical subgroup $ N$ of $ G$, we classify all ergodic, conservative, invariant Radon measures on $ Z$ for the diagonal $ N$-action.


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Additional Information

Amir Mohammadi
Affiliation: Department of Mathemtics, The University of California, San Diego, California 92093
Email: ammohammadi@ucsd.edu

Hee Oh
Affiliation: Department of Mathematics, Yale University, New Haven, Connecticut 06511 – and – Korea Institute for Advanced Study, Seoul, Korea
Email: hee.oh@yale.edu

DOI: https://doi.org/10.1090/proc/13840
Keywords: Geometrically finite groups, measure classification, Radon measures, Burger-Roblin measure
Received by editor(s): April 19, 2016
Received by editor(s) in revised form: June 1, 2017
Published electronically: November 10, 2017
Additional Notes: The first author was supported in part by NSF Grants #1500677, #1724316, and #1128155, and an Alfred P. Sloan Research Fellowship.
The second author was supported in part by NSF Grant #1361673.
Communicated by: Nimish Shah
Article copyright: © Copyright 2017 American Mathematical Society

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