HAUSDORFF DIMENSION OF DIRECTIONAL LIMIT SETS FOR SELF-JOININGS OF HYPERBOLIC MANIFOLDS

. The classical result of Patterson and Sullivan says that for a non-elementary convex cocompact subgroup Γ < SO ◦ ( n, 1), n ≥ 2, the Hausdorff dimension of the limit set of Γ is equal to the critical exponent of Γ. In this paper, we generalize this result for self-joinings of convex cocompact groups in two ways. Let ∆ be a finitely generated group and ρ i : ∆ → SO ◦ ( n i , 1) be a convex cocompact faithful representation of ∆ for 1 ≤ i ≤ k . Associated to ρ = ( ρ 1 , · · · , ρ k ), we consider the following self-joining subgroup of (cid:81) that ρ i is critical exponent of ρ i (∆). where of Γ.