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- W4367694630 abstract "Let $G$ be a connected semisimple real algebraic group and $Gamma<G$ be its Zariski dense discrete subgroup. We prove that if $Gammabackslash G$ admits any finite Bowen-Margulis-Sullivan measure, then $Gamma$ is virtually a product of higher rank lattices and discrete subgroups of rank one factors of $G$. This may be viewed as a measure-theoretic analogue of classification of convex cocompact actions by Kleiner-Leeb and Quint, which was conjectured by Corlette in 1994. The key ingredients in our proof are the product structure of leafwise measures and the high entropy method of Einsiedler-Katok-Lindenstrauss. In a companion paper jointly with Edwards and Oh, we use this result to show that the bottom of the $L^2$ spectrum has no atom in any infinite volume quotient of a higher rank simple algebraic group." @default.
- W4367694630 created "2023-05-03" @default.
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- W4367694630 date "2023-04-30" @default.
- W4367694630 modified "2023-10-15" @default.
- W4367694630 title "Discrete subgroups with finite Bowen-Margulis-Sullivan measure in higher rank" @default.
- W4367694630 doi "https://doi.org/10.48550/arxiv.2305.00610" @default.
- W4367694630 hasPublicationYear "2023" @default.
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