10/15/2004

Colin Guillarmou
Purdue University

Resolvent and scattering theory on asymptotically hyperbolic manifolds

We will review scattering theory on a class of complete manifolds with asymptotically negative constant curvatures. We will give a sufficient and necessary condition on the metric to obtain a meromorphic extension of the resolvent for the Laplacian to the complex plane and will see that essential singularities can appear without this condition. Finally we will explain the relations between scattering poles and resonances, with applications to asymptotically Einstein manifolds and convex co-compact hyperbolic manifolds.