Higher dimensional Scherk's hypersurfaces
Abstract
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- September 2001
- DOI:
- 10.48550/arXiv.math/0109131
- arXiv:
- arXiv:math/0109131
- Bibcode:
- 2001math......9131P
- Keywords:
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- Differential Geometry;
- Analysis of PDEs;
- 53A07;
- 53A10
- E-Print:
- 22 pages. Improved version