Kenichi Ito: Absence of embedded eigenvalues for Riemannian Laplacians

We consider a Riemannian manifold with, at least, one expanding end, and prove the absence of L²-eigenvalues for the Schrödinger operator above some critical value. The critical value is computed from the volume growth rate of the end and the potential behavior at infinity. The end structure is formulated abstractly in terms of some convex function, and the examples include asymptotically Euclidean and hyperbolic ends. This talk is based on a joint work with E.Skibsted (Aarhus University).