For a conformally compact manifold that is hyperbolic near infinity and of
dimension n+1, we complete the proof of the optimal O(rn+1) upper bound
on the resonance counting function, correcting a mistake in the existing
literature. In the case of a compactly supported perturbation of a hyperbolic
manifold, we establish a Poisson formula expressing the regularized wave trace
as a sum over scattering resonances. This leads to an rn+1 lower bound on
the counting function for scattering poles.Comment: 29 pages, minor corrections, added one figur