On 3D manifolds close to constant negative curvature, wave solutions decay like t^{-1} and Schrödinger solutions like t^{-3/2}, with small metric and potential perturbations allowed.
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Dispersive estimates for Schr\"{o}dinger's and wave equations on Riemannian manifolds
On 3D manifolds close to constant negative curvature, wave solutions decay like t^{-1} and Schrödinger solutions like t^{-3/2}, with small metric and potential perturbations allowed.