Compact complete minimal immersions in R^3
| dc.creator | Alarcon, Antonio | |
| dc.date | 2007-11-15 | |
| dc.date | 2009-02-10 | |
| dc.date.accessioned | 2026-07-07T12:39:02Z | |
| dc.date.available | 2026-07-07T12:39:02Z | |
| dc.description | In this paper we find, for any arbitrary finite topological type, a compact Riemann surface $\mathcal{M},$ an open domain $M\subset\mathcal{M}$ with the fixed topological type, and a conformal complete minimal immersion $X:M\to\R^3$ which can be extended to a continuous map $X:\bar{M}\to\R^3,$ such that $X_{|\partial M}$ is an embedding and the Hausdorff dimension of $X(\partial M)$ is $1.$ We also prove that complete minimal surfaces are dense in the space of minimal surfaces spanning a finite set of closed curves in $\R^3$, endowed with the topology of the Hausdorff distance. | |
| dc.description | 16 pages. Main theorem improved. To appear in Trans. Amer. Math. Soc | |
| dc.identifier | https://arxiv.org/abs/0711.2394 | |
| dc.identifier | http://arxiv.org/abs/0711.2394 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/218971 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A10; 53C42; 49Q05; 49Q10 | |
| dc.title | Compact complete minimal immersions in R^3 | |
| dc.type | text |