Existence and Scattering for Solutions to Semilinear Wave Equations on   High Dimensional Hyperbolic Space
  We prove small-data global existence to semi-linear wave equations on hyperbolic space of dimension greater than or equal to three, for nonlinearities that have the form of a sufficiently high integer power of the solution. We also prove the existence and asymptotic completeness of wave operators in this setting. 
Amanda French
math.AP