  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.
