Absence of embedded eigenvalues for Riemannian Laplacians

Hamiltonians in Magnetic Fields

25 October 15:30 - 16:30

Kenichi Ito - Kobe University

We consider a Riemannian manifold with, at least, one expanding end, and prove the absence of $L^2$-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).
Rafael D. Benguria
Pontificia Universidad Católica de Chile
Arne Jensen
Aalborg University
Georgi Raikov
Pontificia Universidad Católica de Chile
Grigori Rozenblioum
Chalmers/University of Gothenburg
Jan Philip Solovej
University of Copenhagen