A Schwarz-type formula for minimal surfaces in Euclidean space n
Comptes Rendus. Mathématique, Volume 334 (2002) no. 5, pp. 389-394.

This paper introduces a complex representation for minimal surfaces in n , based on the Schwarz formula which solves the classical Björling problem for minimal surfaces in 3 . As an application, it is shown that a k-dimensional plane of n is a plane of symmetry of a minimal surface in n provided it intersects the surface orthogonally. A procedure for the construction of minimal surfaces is also described. This procedure introduces minimal surfaces with prescribed geometric properties, starting from real analytic curves in n .

Cet article présente une représentation complexe des surfaces minimales de n , basée sur la formule de Schwarz qui résout le problème classique de Björling pour les surfaces minimales de 3 . Comme application, nous montrons qu'un plan de dimension k de n est un plan de symetrie d'une surface minimale de n s'il lui est orthogonal. Nous décrivons aussi un procédé de construction de surfaces minimales ayant des propriétés géométriques prédéterminées, à partir de courbes analytiques réelles.

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DOI: 10.1016/S1631-073X(02)02280-X
Alı́as, Luis J. 1; Mira, Pablo 2

1 Departamento de Matemáticas, Universidad de Murcia, 30100 Espinardo, Murcia, Spain
2 Departamento de Matemática Aplicada y Estadı́stica, Universidad Politécnica de Cartagena, 30203 Cartagena, Murcia, Spain
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     title = {A {Schwarz-type} formula for minimal surfaces in {Euclidean} space $ \mathbb{R}^{n}$},
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Alı́as, Luis J.; Mira, Pablo. A Schwarz-type formula for minimal surfaces in Euclidean space $ \mathbb{R}^{n}$. Comptes Rendus. Mathématique, Volume 334 (2002) no. 5, pp. 389-394. doi : 10.1016/S1631-073X(02)02280-X. http://www.numdam.org/articles/10.1016/S1631-073X(02)02280-X/

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