An Introduction to Classical and Modern Minimal Surface Theory

By Peter McGrath

May 6, 2013

Abstract

After introducing several equivalent definitions of what it means for an immersion to be minimal, I will discuss some maximum principle has been applied in geometry, in particular to the Half Space theorem of Hoffman and Meeks. Time permitting, I will discuss some recent results - the Positive Mass theorem of Schoen and Yau and Brendle's proof of the Lawson Conjecture.