Weakly Type-Preserving Sequences and Strong Convergence

Jørgensen conjectured that if there are no new parabolics in the algebraic limit of a sequence of Kleinian groups then the sequence should converge strongly. We verify this conjecture in the case that the algebraic limit has non-empty domain of discontinuity. An immediate corollary under the same assumptions is that any sequence converging algebraically to a minimally parabolic limit converges strongly.