  We provide reversed Strichartz estimates for the shifted wave equations on
non-trapping asymptotically hyperbolic manifolds using cluster estimates for
spectral projectors proved previously in such generality. As a consequence, we
solve a problem left open in \cite{SSWZ} about the endpoint case for global
well-posedness of nonlinear wave equations. We also provide estimates in this
context for the maximal wave operator.
