  We apply Mourre theory to compatible Laplacians on manifolds with corners of
codimension 2 in order to prove absence of singular spectrum, that
non-threshold eigenvalues have finite multiplicity and could accumulate only at
thresholds or infinity. It turns out that we need Mourre estimates on manifolds
with cylindrical ends where the results are both expected and consequences of
more general theorems. In any case we also provide a description, interesting
in its own, of Mourre theory in such context that makes our text complete and
suggests generalizations to higher order codimension corners. We use theorems
of functional analysis that are suitable for these geometric applications.
