The spectrum of magnetic Schrödinger operators and $k$-form Laplacians on conformally cusp manifolds
| dc.creator | Golénia, Sylvain | |
| dc.creator | Moroianu, Sergiu | |
| dc.date | 2005-07-21 | |
| dc.date.accessioned | 2026-07-07T05:21:53Z | |
| dc.date.available | 2026-07-07T05:21:53Z | |
| dc.description | We consider open manifolds which are interiors of a compact manifold with boundary, and Riemannian metrics asymptotic to a conformally cylindrical metric near the boundary. We show that the essential spectrum of the Laplace operator on functions vanishes under the presence of a magnetic field which does not define an integral relative cohomology class. It follows that the essential spectrum is not stable by perturbation even by a compactly supported magnetic field. We also treat magnetic operators perturbed with electric fields. In the same context we describe the essential spectrum of the $k$-form Laplacian. This is shown to vanish precisely when the $k$ and $k-1$ de Rham cohomology groups of the boundary vanish. In all the cases when we have pure-point spectrum we give Weyl-type asymptotics for the eigenvalue-counting function. In the other cases we describe the essential spectrum. | |
| dc.description | 32 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0507443 | |
| dc.identifier | http://arxiv.org/abs/math/0507443 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75855 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.subject | Spectral Theory | |
| dc.subject | 58J40; 58Z05 | |
| dc.title | The spectrum of magnetic Schrödinger operators and $k$-form Laplacians on conformally cusp manifolds | |
| dc.type | text |