The case of equality in the dichotomy of Mohammadi-Oh

Abstract

If n≥3 and Γ is a convex-cocompact Zariski-dense discrete subgroup of SOo(1,n+1) such that δΓ=n−m where m is an integer, 1≤m≤n−1, we show that for any m-dimensional subgroup U in the horospheric group N, the Burger-Roblin measure associated to Γ on the quotient of the frame bundle is U-recurrent.