Decay estimates for the Schroedinger evolution on asymptotically conic   surfaces of revolution I
  We establish a dispersive estimate (with a decay of 1/t), valid for all times, for the Schroedinger evolution on a non-compact 2-dimensional manifold with a trapped geodesic. 
Wilhelm Schlag (University of Chicago), Avy Soffer (Rutgers   University), Wolfgang Staubach (University of Chicago)