Invariant Radon measures for Unipotent flows and products of Kleinian groups

Amir Mohammadi; Hee Oh

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arXiv · 1510.03504

Invariant Radon measures for Unipotent flows and products of Kleinian groups

Amir Mohammadi·Hee Oh

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Abstract

Let G=PSL(2, F) where F= R or C, and consider the space Z=(\Gamma_1 x \Gamma_2)\ (G x G) where \Gamma_1<G is a co-compact lattice and \Gamma_2<G is a finitely generated discrete Zariski dense subgroup. The work of Benoist-Quint gives a classification of all ergodic invariant Radon measures on Z for the diagonal G-action. In this paper, for a horospherical subgroup N of G, we classify all ergodic, conservative, invariant Radon measures on Z for the diagonal N-action, under the additional assumption that \Gamma_2 is geometrically finite.

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Amir Mohammadi, Hee Oh. 2015-10-13. Invariant Radon measures for Unipotent flows and products of Kleinian groups. https://arxiv.org/abs/1510.03504

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