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arXiv · 2008.05429

Horospherically invariant measures and finitely generated Kleinian groups

Or Landesberg
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Abstract

Let $ Γ< PSL_2(\mathbb{C}) $ be a Zariski dense finitely generated Kleinian group. We show all Radon measures on $ PSL_2(\mathbb{C}) / Γ$ which are ergodic and invariant under the action of the horospherical subgroup are either supported on a single closed horospherical orbit or quasi-invariant with respect to the geodesic frame flow and its centralizer. We do this by applying a result of Landesberg and Lindenstrauss together with fundamental results in the theory of 3-manifolds, most notably the Tameness Theorem by Agol and Calegari-Gabai.

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Or Landesberg. 2021-02-28. Horospherically invariant measures and finitely generated Kleinian groups. https://arxiv.org/abs/2008.05429

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