Resolvent estimate for asymptotically hyperbolic surfaces without evenness assumption

Abstract

We prove a sharp cut-off resolvent estimate for the Laplacian on non-compact Riemannian manifolds whose ends satisfy the Cardoso--Vodev assumption and whose geometry near the trapped set agrees with that of an even asymptotically hyperbolic manifold with the corresponding resolvent estimate. As applications, we show the global Strichartz and spectral projection estimates on negatively curved asymptotically hyperbolic surfaces, without assuming the evenness at infinity.