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.
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.
Revised:
Accepted:
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Keywords: Minimal surfaces, Min-Max theory, Plateau problem
Mot 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}, pages = {1909--1986}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {68}, number = {5}, year = {2018}, doi = {10.5802/aif.3200}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.3200/} }
TY - JOUR AU - De Lellis, Camillo AU - Ramic, Jusuf TI - Min-max theory for minimal hypersurfaces with boundary JO - Annales de l'Institut Fourier PY - 2018 SP - 1909 EP - 1986 VL - 68 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.3200/ DO - 10.5802/aif.3200 LA - en ID - AIF_2018__68_5_1909_0 ER -
%0 Journal Article %A De Lellis, Camillo %A Ramic, Jusuf %T Min-max theory for minimal hypersurfaces with boundary %J Annales de l'Institut Fourier %D 2018 %P 1909-1986 %V 68 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.3200/ %R 10.5802/aif.3200 %G en %F AIF_2018__68_5_1909_0
De Lellis, Camillo; Ramic, Jusuf. Min-max theory for minimal hypersurfaces with boundary. Annales de l'Institut Fourier, Volume 68 (2018) no. 5, pp. 1909-1986. doi : 10.5802/aif.3200. http://archive.numdam.org/articles/10.5802/aif.3200/
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