Duke Mathematical Journal

Classification of joinings for Kleinian groups

Amir Mohammadi and Hee Oh

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We classify all locally finite joinings of a horospherical subgroup action on ΓG when Γ is a Zariski-dense geometrically finite subgroup of G=PSL2(R) or PSL2(C). This generalizes Ratner’s 1983joining theorem for the case when Γ is a lattice in G. One of the main ingredients is equidistribution of nonclosed horospherical orbits with respect to the Burger–Roblin measure, which we prove in a greater generality where Γ is any Zariski-dense geometrically finite subgroup of G=SO(n,1), n2.

Article information

Duke Math. J., Volume 165, Number 11 (2016), 2155-2223.

Received: 20 September 2014
Revised: 8 September 2015
First available in Project Euclid: 21 April 2016

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Zentralblatt MATH identifier

Primary: 37A17: Homogeneous flows [See also 22Fxx]
Secondary: 11N45: Asymptotic results on counting functions for algebraic and topological structures 57M60: Group actions in low dimensions 20F67: Hyperbolic groups and nonpositively curved groups 37F35: Conformal densities and Hausdorff dimension 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]

geometrically finite hyperbolic groups joining Burger–Roblin measure Bowen–Margulis–Sullivan measure


Mohammadi, Amir; Oh, Hee. Classification of joinings for Kleinian groups. Duke Math. J. 165 (2016), no. 11, 2155--2223. doi:10.1215/00127094-3476807. https://projecteuclid.org/euclid.dmj/1461252849

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