2011/12/13 by Leonardo A. Cano García, García, Leonardo A. Cano
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1112.2947
openalex publication_date 2011/12/13 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28
We apply Mourre theory to compatible Laplacians on manifolds with corners of\ncodimension 2 in order to prove absence of singular spectrum, that\nnon-threshold eigenvalues have finite multiplicity and could accumulate only at\nthresholds or infinity. It turns out that we need Mourre estimates on manifolds\nwith cylindrical ends where the results are both expected and consequences of\nmore general theorems. In any case we also provide a description, interesting\nin its own, of Mourre theory in such context that makes our text complete and\nsuggests generalizations to higher order codimension corners. We use theorems\nof functional analysis that are suitable for these geometric applications.\n