On the spectrum of $\bar{X}$-bounded minimal submanifolds
| dc.creator | Salavessa, Isabel M. C. | |
| dc.date | 2009-01-09 | |
| dc.date | 2009-01-14 | |
| dc.date.accessioned | 2026-07-07T12:28:51Z | |
| dc.date.available | 2026-07-07T12:28:51Z | |
| dc.description | We prove, under a certain boundedness condition at infinity on the $(\bar{X}^{\top}, \bar{X}^{\bot})$-component of the second fundamental form, the vanishing of the essential spectrum of a complete minimal $\bar{X}$-bounded and $\bar{X}$-properly immersed submanifold on a Riemannian manifold endowed with a strongly convex vector field $\bar{X}$. The same conclusion also holds for any complete minimal $h$-bounded and $h$-properly immersed submanifold that lies in a open set of a Riemannian manifold $\oM$ supporting a nonnegative strictly convex function $h$. This extends a recent result of Bessa, Jorge and Montenegro on the spectrum of Martin-Morales minimal surfaces. Our proof uses as main tool an extension of Barta's theorem given in \cite{BM} | |
| dc.description | v.2 13 pages. We improve some theorems, correct some misprints and add a new theorem (theorem 5) in section 2 that shows complete bounded minimal immersed submanifolds have unbounded second fundamental form, for suitable curvature conditions of the ambient space | |
| dc.identifier | https://arxiv.org/abs/0901.1246 | |
| dc.identifier | http://arxiv.org/abs/0901.1246 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/215679 | |
| dc.subject | Differential Geometry | |
| dc.subject | Spectral Theory | |
| dc.subject | 53C40; 58C40 | |
| dc.title | On the spectrum of $\bar{X}$-bounded minimal submanifolds | |
| dc.type | text |