Distribution of resonances for analytic asymptotically hyperbolic spaces

Abstract

For a class of asymptotically hyperbolic metrics on the unit ball ${\mathbb{B}}^3$, we study the meromorphic properties of the resolvent of the Laplacian. In particular, we prove the existence of logarithmic type regions free of resonances (poles of the resolvent). Also, away from the region where the resonances may accumulate, we obtain a polynomial bound on the growth of the number of resonances in disks.