Min-max constructions of 2d-minimal surfaces

Abstract

In this thesis we will present a proof of the existence of closed embedded minimal surfaces in a closed 3-dimensional manifold constructed via min-max arguments and we will prove genus bounds for the produced surfaces. A stronger estimate was announced by Pitts and Rubinstein but to our knowledge its proof has never been published. Our proof follows ideas of Simon and uses an extension of a famous result of Meeks, Simon and Yau on the convergence of minimizing sequences of isotopic surfaces. Eine Minimalfläche ist eine Fläche im Ra Show more