no. 5
Min-max theory for minimal hypersurfaces with boundary
[Methodes de Min-max pour hypersurfaces minimales ayant le bord donné]
De Lellis, Camillo1 ; Ramic, Jusuf1
1 Institut für Mathematik Universität Zürich Winterthurerstrasse 190 CH-8057 Zürich (Switzerland)
Annales de l'Institut Fourier, Tome 68 (2018) no. 5, pp. 1909-1986.

Dans ce travail nous proposons une théorie « de Min-Max » pour hypersurfaces plongées ayant un bord prescrit. Nous donnons plusieurs applications de cette théorie à l’existence de solutions du problème de Plateau. Des variantes plus simple des nos théoremes sont aussi valides pour les hypersurfaces minimales avec frontière libre.

In this note we propose a min-max theory for embedded hypersurfaces with a fixed boundary and apply it to prove several theorems about the existence of embedded minimal hypersurfaces with a given boundary. A simpler variant of these theorems holds also for the case of the free boundary minimal surfaces.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3200
Classification : 53C42, 49Q05, 53A10
Keywords: Minimal surfaces, Min-Max theory, Plateau problem
Mots-clés : Surfaces minimales, Théorie de Min-Max, problème de Plateau

De Lellis, Camillo 1 ; Ramic, Jusuf 1

1 Institut für Mathematik Universität Zürich Winterthurerstrasse 190 CH-8057 Zürich (Switzerland)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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De Lellis, Camillo; Ramic, Jusuf. Min-max theory for minimal hypersurfaces with boundary. Annales de l'Institut Fourier, Tome 68 (2018) no. 5, pp. 1909-1986. doi : 10.5802/aif.3200. https://aif.centre-mersenne.org/articles/10.5802/aif.3200/

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