Absence of embedded eigenvalues for the Schrödinger operator on manifold (Spectral and Scattering Theory and Related Topics)

Abstract

We discuss the absence of eigenvalues above some critical energy for the Schrödinger operator on a manifold with asymptotically Euclidean and/or hyperbolic ends. The critical energy can be computed only by the geometry of the ends. The main ingredients of proof are the super-exponential decay estimates for eigenfunctions and the absence of super-exponentially decaying eigenfunctions.