English

Min-max theory for minimal hypersurfaces with boundary

Analysis of PDEs 2017-05-19 v2

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.

Keywords

Cite

@article{arxiv.1611.00926,
  title  = {Min-max theory for minimal hypersurfaces with boundary},
  author = {Camillo De Lellis and Jusuf Ramic},
  journal= {arXiv preprint arXiv:1611.00926},
  year   = {2017}
}

Comments

58 pages, 4 figures. Second version with errors corrected, following the comments of a referee

R2 v1 2026-06-22T16:40:39.148Z