Convergence properties of end invariants
  We prove a continuity property for ending invariants of convergent sequences of Kleinian surface groups. We also analyze the bounded curve sets of such groups and show that their projections to non-annular subsurfaces lie a bounded Hausdorff distance from geodesics joining the projections of the ending invariants. 
Jeffrey F. Brock, Kenneth W. Bromberg, Richard D. Canary, Yair N.   Minsky
math.GT math.DG