We study the long time behavior of radial solutions to nonlinear Schrödinger equations on hyperbolic space. We show that the usual distinction between short range and long range nonlinearity is modified: the geometry of the hyperbolic space makes every power-like nonlinearity short range. The proofs rely on weighted Strichartz estimates, which imply Strichartz estimates for a broader family of ...

The Schwarzschild and Reissner-Nordstrøm soutions to Einstein’s equations describe space-times which contain spherically symmetric black holes. We consider solutions to the liear wave equation in the exterior of a fixed blackhole spacetime of this type. We show that for solutions with initial data which decay at infinite, a weighted L norm in space decays like t− 1 3 . This weight vanishes at t...