On embeddedness of area-minimizing disks, and an application to constructing complete minimal surfaces
| dc.creator | Rossman, Wayne | |
| dc.date | 2008-04-26 | |
| dc.date.accessioned | 2026-07-07T09:35:29Z | |
| dc.date.available | 2026-07-07T09:35:29Z | |
| dc.description | Let $α$ be a polygonal Jordan curve in $\bfR^3$. We show that if $α$ satisfies certain conditions, then the least-area Douglas-Radó disk in $\bfR^3$ with boundary $α$ is unique and is a smooth graph. As our conditions on $α$ are not included amongst previously known conditions for embeddedness, we are enlarging the set of Jordan curves in $\bfR^3$ which are known to be spanned by an embedded least-area disk. As an application, we consider the conjugate surface construction method for minimal surfaces. With our result we can apply this method to a wider range of complete catenoid-ended minimal surfaces in $\bfR^3$. | |
| dc.identifier | https://arxiv.org/abs/0804.4208 | |
| dc.identifier | http://arxiv.org/abs/0804.4208 | |
| dc.identifier | J. Math. Soc. Japan 52(1) (2000), 25-40 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159847 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A10; 53A05; 53C42 | |
| dc.title | On embeddedness of area-minimizing disks, and an application to constructing complete minimal surfaces | |
| dc.type | text |