Absence of singular continuous spectrum for some geometric Laplacians

We provide two examples of spectral analysis techniques of Schroedinger operators applied to geometric Laplacians. In particular we show how to adapt the method of analytic dilation to Laplacians on complete manifolds with corners of codimension 2 finding the absence of singular continuous spectrum for these operators, a description of the behavior of its pure point spectrum in terms of the underlying geometry, and a theory of quantum resonances.
Comment: survey of techniques used to prove absence of singular spectrum on manifolds with cylindrical ends and the generalization of one of them, analytic dilation, to complete manifolds with corners