DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, March 29 Padelford C-36 3:45 pm

Semiclassical estimates in asymptotically Euclidean scattering

András Vasy (University of California at Berkeley)

I will discuss joint work with M. Zworski in which we obtain semiclassical resolvent estimates for non-trapping long range perturbations of the Laplacian on asymptotically Euclidean manifolds. Our proof is based on a positive commutator argument which differs from Mourretype estimates by making the commutant also positive. The resolvent estimates, including the weighting of the Sobolev spaces in the estimates, are an immediate consequence.