Year: 2025
Type: article
Abstract: Let G be a connected semisimple real algebraic group and < G be a Zariski dense discrete subgroup.We prove that if nG admits any finite Bowen-Margulis-Sullivan measure, then is virtually a product of higher rank lattices and discrete subgroups of rank one factors of G.This may be viewed as a measuretheoretic analogue of the classification of convex cocompact actions by Kleiner and Leeb (Invent. Math. 163 (2006) 657-676) and Quint (Geom. Dedicata 113 (2005) 1-19), 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 and Lindenstrauss (Ann. of Math. 164 (2006) 513-560).In a companion paper jointly with Edwards and Oh (C. R. Math. Acad. Sci. Paris 362 (2024) 1873-1880) 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.
Source: Geometry & Topology
Authors: Mikołaj Frączyk, Minju Lee
Institutions: Jagiellonian University, University of Chicago
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4409717459