Min-max theory for minimal hypersurfaces with boundary
arXiv:1611.00926
Abstract
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.
58 pages, 4 figures. Second version with errors corrected, following the comments of a referee