Higher dimensional Scherk's hypersurfaces

Details Higher dimensional Scherk's hypersurfaces Higher dimensional Scherk's hypersurfaces

2001-09-19

arxiv.org/abs/math/0109131v2

Mathematics

Differential Geometry

22 pages. Improved version

Scientific paper

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.

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