Min-max theory for minimal hypersurfaces with boundary  [ Methodes de Min-max pour hypersurfaces minimales ayant le bord donné ]
Annales de l'Institut Fourier, Tome 68 (2018) no. 5, p. 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 : 2016-11-18
Révisé le : 2017-05-13
Accepté le : 2017-11-07
Publié le : 2018-11-23
DOI : https://doi.org/10.5802/aif.3200
Classification:  53C42,  49Q05,  53A10
Mots clés: Surfaces minimales, Théorie de Min-Max, problème de Plateau
@article{AIF_2018__68_5_1909_0,
     author = {De Lellis, Camillo and Ramic, Jusuf},
     title = {Min-max theory for minimal hypersurfaces with boundary},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {5},
     year = {2018},
     pages = {1909-1986},
     doi = {10.5802/aif.3200},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2018__68_5_1909_0}
}
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/item/AIF_2018__68_5_1909_0/

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