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 12 Apr 2026

[BibTeX]

Published Paper

Inserted: 2 nov 2016
Last Updated: 12 apr 2026

Journal: Annales de l'Institut Fourier (Grenoble)
Volume: 68
Number: 5
Pages: 1909-1986
Year: 2018

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.


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