## Journal of Differential Geometry

### The existence of embedded minimal hypersurfaces

#### Abstract

We give a shorter proof of the existence of nontrivial closed minimal hypersurfaces in closed smooth $(n + 1)$-dimensional Riemannian manifolds, a theorem proved first by Pitts for $2 \leq n \leq 5$ and extended later by Schoen and Simon to any $n$.

#### Article information

Source
J. Differential Geom., Volume 95, Number 3 (2013), 355-388.

Dates
First available in Project Euclid: 16 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1381931732

Digital Object Identifier
doi:10.4310/jdg/1381931732

Mathematical Reviews number (MathSciNet)
MR3128988

Zentralblatt MATH identifier
1284.53057

#### Citation

De Lellis, Camillo; Tasnady, Dominik. The existence of embedded minimal hypersurfaces. J. Differential Geom. 95 (2013), no. 3, 355--388. doi:10.4310/jdg/1381931732. https://projecteuclid.org/euclid.jdg/1381931732