Calculus of Variations and Geometric Measure Theory

C. De Lellis - J. Ramic

Min-max theory for minimal hypersurfaces with boundary

created by delellis on 02 Nov 2016
modified on 17 Jul 2018


Accepted Paper

Inserted: 2 nov 2016
Last Updated: 17 jul 2018

Journal: To appear in Annales de l'Institut Fourier
Year: 2016


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.