[Une formule de type Schwarz pour les surfaces minimales de l'espace euclidien ]
Cet article présente une représentation complexe des surfaces minimales de , basée sur la formule de Schwarz qui résout le problème classique de Björling pour les surfaces minimales de . Comme application, nous montrons qu'un plan de dimension k de est un plan de symetrie d'une surface minimale de 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.
This paper introduces a complex representation for minimal surfaces in , based on the Schwarz formula which solves the classical Björling problem for minimal surfaces in . As an application, it is shown that a k-dimensional plane of is a plane of symmetry of a minimal surface in 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 .
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@article{CRMATH_2002__334_5_389_0,
author = {Al{\i}́as, Luis J. and Mira, Pablo},
title = {A {Schwarz-type} formula for minimal surfaces in {Euclidean} space $ \mathbb{R}^{n}$},
journal = {Comptes Rendus. Math\'ematique},
pages = {389--394},
publisher = {Elsevier},
volume = {334},
number = {5},
year = {2002},
doi = {10.1016/S1631-073X(02)02280-X},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02280-X/}
}
TY - JOUR
AU - Alı́as, Luis J.
AU - Mira, Pablo
TI - A Schwarz-type formula for minimal surfaces in Euclidean space $ \mathbb{R}^{n}$
JO - Comptes Rendus. Mathématique
PY - 2002
SP - 389
EP - 394
VL - 334
IS - 5
PB - Elsevier
UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02280-X/
DO - 10.1016/S1631-073X(02)02280-X
LA - en
ID - CRMATH_2002__334_5_389_0
ER -
%0 Journal Article
%A Alı́as, Luis J.
%A Mira, Pablo
%T A Schwarz-type formula for minimal surfaces in Euclidean space $ \mathbb{R}^{n}$
%J Comptes Rendus. Mathématique
%D 2002
%P 389-394
%V 334
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S1631-073X(02)02280-X/
%R 10.1016/S1631-073X(02)02280-X
%G en
%F CRMATH_2002__334_5_389_0
Alı́as, Luis J.; Mira, Pablo. A Schwarz-type formula for minimal surfaces in Euclidean space $ \mathbb{R}^{n}$. Comptes Rendus. Mathématique, Tome 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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