## Duke Mathematical Journal

### Classification of joinings for Kleinian groups

#### Abstract

We classify all locally finite joinings of a horospherical subgroup action on $\Gamma\setminus G$ when $\Gamma$ is a Zariski-dense geometrically finite subgroup of $G=\operatorname{PSL}_{2}(\mathbb{R})$ or $\operatorname{PSL}_{2}(\mathbb{C})$. This generalizes Ratner’s 1983joining theorem for the case when $\Gamma$ 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 $\Gamma$ is any Zariski-dense geometrically finite subgroup of $G=\operatorname{SO}(n,1)^{\circ}$, $n\ge2$.

#### Article information

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

Dates
Revised: 8 September 2015
First available in Project Euclid: 21 April 2016

https://projecteuclid.org/euclid.dmj/1461252849

Digital Object Identifier
doi:10.1215/00127094-3476807

Mathematical Reviews number (MathSciNet)
MR3536991

Zentralblatt MATH identifier
1362.37009

#### Citation

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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