Complete subamanifolds of $\mathbb{R}^{n}$ with finite topology
| dc.creator | Bessa, G. Pacelli | |
| dc.creator | Jorge, L. | |
| dc.creator | Montenegro, J. Fabio | |
| dc.date | 2006-01-24 | |
| dc.date.accessioned | 2026-07-07T09:37:08Z | |
| dc.date.available | 2026-07-07T09:37:08Z | |
| dc.description | We show that a complete $m$-dimensional immersed submanifold $M$ of $\mathbb{R}^{n}$ with $a(M)<1$ is properly immersed and have finite topology, where $a(M)\in [0,\infty]$ is an scaling invariant number that gives the rate that the norm of the second fundamental form decays to zero at infinity. The class of submanifolds $M$ with $a(M)<1$ contains all complete minimal surfaces in $\mathbb{R}^{n}$ with finite total curvature, all $m$-dimensional minimal submanifolds $M $ of $ \mathbb{R}^{n}$ with finite total scalar curvature $\smallint_{M}| α|^{m} dV<\infty $ and all complete 2-dimensional complete surfaces with $\smallint_{M}| α|^{2} dV<\infty $ and nonpositive curvature with respect to every normal direction, since $a(M)=0$ for them. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0601582 | |
| dc.identifier | http://arxiv.org/abs/math/0601582 | |
| dc.identifier | Comm. Anal. Geom. vol. 15, n.4 (2007) 725-732 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160351 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C42 | |
| dc.title | Complete subamanifolds of $\mathbb{R}^{n}$ with finite topology | |
| dc.type | text |