Classification of Joinings for Kleinian Groups
نویسنده
چکیده
We classify all locally finite joinings of a horospherical subgroup action on Γ\G when Γ is a Zariski dense geometrically finite subgroup of G = PSL2(R) or PSL2(C). This generalizes Ratner’s 1983 joining theorem for the case when Γ is a lattice in G. One of the main ingredients is equidistribution of non-closed 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)◦, n ≥ 2.
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