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 SO o (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.