Complete proper minimal surfaces in convex bodies of $R^3$
| dc.creator | Martin, Francisco | |
| dc.creator | Morales, Santiago | |
| dc.date | 2004-05-26 | |
| dc.date.accessioned | 2026-07-07T05:08:37Z | |
| dc.date.available | 2026-07-07T05:08:37Z | |
| dc.description | Consider a convex domain B of space. We prove that there exist complete minimal surfaces which are properly immersed in B. We also demonstrate that if D and D' are convex domains with D bounded and the closure of D contained in D' then any minimal disk whose boundary lies in the boundary of D, can be approximated in any compact subdomain of D by a complete minimal disk which is proper in D'. We apply these results to study the so called type problem for a minimal surface: we demonstrate that the interior of any convex region is not a universal region for minimal surfaces, in the sense explained by Meeks and Perez. | |
| dc.description | 26 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/math/0405507 | |
| dc.identifier | http://arxiv.org/abs/math/0405507 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71337 | |
| dc.subject | General Mathematics | |
| dc.subject | Differential Geometry | |
| dc.subject | Primary 53A10; Secondary 49Q05, 49Q10, 53C42 | |
| dc.title | Complete proper minimal surfaces in convex bodies of $R^3$ | |
| dc.type | text |