Elliptische Funktionen und vollständige Minimalflächen.
Elliptische und hyperelliptische Funktionen und vollständige Minimalflächen vom Enneperschen Typ.
Embedde minimal annuli in R3 bounded by a pair of straight lines.
Embedded, doubly periodic minimal surfaces.
Embedded Minimal Disks with a Free Boundary on a Polyhedron in IR3.
Embedded minimal surfaces derived from Scherk's Examples.
Embedded minimal surfaces with an infinite number of ends.
Embeddedness and uniqueness of minimal surfaces solving a partially free boundary value problem.
End-to-end gluing of constant mean curvature hypersurfaces
It was observed by R. Kusner and proved by J. Ratzkin that one can connect together two constant mean curvature surfaces having two ends with the same Delaunay parameter. This gluing procedure is known as a “end-to-end connected sum”. In this paper we generalize, in any dimension, this gluing procedure to construct new constant mean curvature hypersurfaces starting from some known hypersurfaces.
Estimates for Evolutionary Surfaces of Prescribed Mean Curvature.
Estimation of the best constant involving the norm of the higher-order Wente problem.
Estimations of the best constant involving the norm in Wente’s inequality and compact -surfaces in euclidean space
Estimations of the best constant involving the L2 norm in Wente's inequality and compact H-surfaces in Euclidean space
In the first part of this paper, we study the best constant involving the L2 norm in Wente's inequality. We prove that this best constant is universal for any Riemannian surface with boundary, or respectively, for any Riemannian surface without boundary. The second part concerns the study of critical points of the associate energy functional, whose Euler equation corresponds to H-surfaces. We will establish the existence of a non-trivial critical point for a plan domain with small holes.
Exemples d'applications holomorphes d'indice un
Nous construisons une famille de surfaces de Riemann hyperelliptiques, de genre variable, munies de fonctions méromorphes de degré deux et d’indice un, ce qui apporte une réponse positive à une conjecture de S. Montiel et A. Ros.
Existence and Non Existence of Capillary Surfaces.
Existence and regularity of hypersurfaces with prescribed mean curvature and a free boundary.
Existence and regularity of weak solutions to the prescribed mean curvature equation for a nonparametric surface.
Existence de surfaces de Willmore qui ne sont pas minimales
Existence of embedded solutions of Plateau's problem
Existence of H-bubbles in a perturbative setting.
Given a C1 function H: R3 --> R, we look for H-bubbles, i.e., surfaces in R3 parametrized by the sphere S2 with mean curvature H at every regular point..