Mourre estimates for compatible Laplacians on complete manifolds with corners of codimension 2

Abstract

We apply Mourre theory to compatible Laplacians on complete manifolds with corners of codimension 2 in order to prove absence of singular continuous spectrum, that non-threshold eigenvalues have finite multiplicity and can 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 this context that makes our text complete and suggests generalizations to manifolds with corners of higher order codimension. We use theorems of functional analysis that are suitable for these geometric applications.