Higher dimensional Scherk's hypersurfaces
Year: 2001
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Pacard, Frank
Institution: Laboratoire d’Analyse et de Mathématiques Appliquées
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949993172