Higher dimensional Scherk's hypersurfaces
| dc.creator | Pacard, Frank | |
| dc.date | 2001-09-19 | |
| dc.date | 2001-11-15 | |
| dc.date.accessioned | 2026-07-07T04:43:27Z | |
| dc.date.available | 2026-07-07T04:43:27Z | |
| dc.description | In 3-dimensional Euclidean space, Scherk second surfaces are singly periodic embedded minimal surfaces with four planar ends. In this paper, we obtain a natural generalization of these minimal surfaces in any higher dimensional Euclidean space ${\R}^{n+1}$, for $n \geq 3$. More precisely, we show that there exist $(n-1)$-periodic embedded minimal hypersurfaces with four hyperplanar ends. The moduli space of these hypersurfaces forms a 1-dimensional fibration over the moduli space of flat tori in ${\R}^{n-1}$. A partial description of the boundary of this moduli space is also given. | |
| dc.description | 22 pages. Improved version | |
| dc.identifier | https://arxiv.org/abs/math/0109131 | |
| dc.identifier | http://arxiv.org/abs/math/0109131 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62226 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 53A07; 53A10 | |
| dc.title | Higher dimensional Scherk's hypersurfaces | |
| dc.type | text |