On the spectrum of a finite-volume negatively-curved manifold
| dc.creator | Lott, John | |
| dc.date | 1999-08-26 | |
| dc.date | 2000-09-10 | |
| dc.date.accessioned | 2026-07-07T05:30:29Z | |
| dc.date.available | 2026-07-07T05:30:29Z | |
| dc.description | We show that a noncompact manifold with bounded sectional curvature, whose ends are sufficiently Gromov-Hausdorff close to rays, has a finite dimensional space of square-integrable harmonic forms. In the special case of a finite-volume manifold with pinched negative sectional curvature, we show that the essential spectrum of the p-form Laplacian is the union of the essential spectra of a collection of ordinary differential operators associated to the ends. We give examples of such manifolds with curvature pinched arbitrarily close to -1 and with an infinite number of gaps in the spectrum of the function Laplacian. | |
| dc.description | 17 pages, statement of Theorem 2 improved | |
| dc.identifier | https://arxiv.org/abs/math/9908136 | |
| dc.identifier | http://arxiv.org/abs/math/9908136 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79009 | |
| dc.subject | Differential Geometry | |
| dc.title | On the spectrum of a finite-volume negatively-curved manifold | |
| dc.type | text |