Higher dimensional Scherk's hypersurfaces
Abstract
In 3dimensional 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 $(n1)$periodic embedded minimal hypersurfaces with four hyperplanar ends. The moduli space of these hypersurfaces forms a 1dimensional fibration over the moduli space of flat tori in ${\R}^{n1}$. A partial description of the boundary of this moduli space is also given.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2001
 arXiv:
 arXiv:math/0109131
 Bibcode:
 2001math......9131P
 Keywords:

 Differential Geometry;
 Analysis of PDEs;
 53A07;
 53A10
 EPrint:
 22 pages. Improved version