The min-max construction of minimal hypersurfaces in closed Riemannian manifolds

Abstract

This thesis is an expository account of the min-max construction of minimal hypersurfaces in closed Riemannian manifolds, following the paper of De Lellis and Tasnady. In the first part, we recall basic facts about the relevant objects from geometric measure theory: sets of finite perimeter and varifolds. In the second and main part, we give the proof of the min-max theorem.