Calculus of Variations and Geometric Measure Theory
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C. De Lellis - J. Ramic

Min-max theory for minimal hypersurfaces with boundary

created by delellis on 02 Nov 2016
modified on 18 May 2017



Inserted: 2 nov 2016
Last Updated: 18 may 2017

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.


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