We classify all locally finite joinings of a horospherical subgroup action on when is a Zariski-dense geometrically finite subgroup of or . This generalizes Ratner’s 1983joining theorem for the case when is a lattice in . 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 is any Zariski-dense geometrically finite subgroup of , .
"Classification of joinings for Kleinian groups." Duke Math. J. 165 (11) 2155 - 2223, 15 August 2016. https://doi.org/10.1215/00127094-3476807