Inserted: 6 may 2011
Last Updated: 2 jul 2013
Journal: To appear in Jour. Diff. Geom.
For the update version and eventual errata see the webpage http:/www.math.uzh.chdelellis
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 $n$.