Higher dimensional Scherk's hypersurfaces - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Article Dans Une Revue Journal de Mathématiques Pures et Appliquées Année : 2002

Higher dimensional Scherk's hypersurfaces

Résumé

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.

Dates et versions

hal-00127006 , version 1 (27-01-2007)

Identifiants

Citer

Frank Pacard. Higher dimensional Scherk's hypersurfaces. Journal de Mathématiques Pures et Appliquées, 2002, 81, pp.241-258. ⟨hal-00127006⟩
84 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More