Global Existence of Small Equivariant Wave Maps on Rotationally Symmetric Manifolds

We introduce a class of rotationally invariant manifolds, which we call admissible, on which the wave flow satisfies smoothing and Strichartz estimates. We deduce the global existence of equivariant wave maps from admissible manifolds to general targets, for small initial data of critical regularity H-n/2. The class of admissible manifolds includes in particular asymptotically flat manifolds and perturbations of real hyperbolic spaces H-n for n >= 3.