Minimal Surfaces and Geometric Measure Theory

Specialeforsvar ved Søren Holst Hansen

Titel: Minimal Surfaces and Geometric Measure Theory 

Abstract: In this thesis we will develop the theory of minimal surfaces from the point of view of geometric measure theory. We will first look at minimal surfaces in 3 dimensions, and then generalize the tools and concepts to higher dimensions and more general classes of surfaces. We will develop the basics of geometric measure theory, that will lay the groundwork for introducing rectifiable varifolds, and we shall see various results on the regularity of varifolds, culminating in the main theorem of the thesis, the Allard regularity theorem. 

Vejleder: Niels Martin Møller
Censor:  Steen Markvorsen, DTU