The existence of embedded minimal hypersurfaces

TL;DR

This paper provides a more concise proof for the existence of nontrivial closed minimal hypersurfaces in closed smooth Riemannian manifolds, building on foundational work by Pitts and Schoen-Simon.

Contribution

It offers a shorter, more streamlined proof of a classical existence theorem for minimal hypersurfaces in Riemannian geometry.

Findings

Simplified proof of minimal hypersurface existence

Extends classical results with a more concise approach

Applicable for all dimensions up to n+1

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 $n$.