A new compactness theory for minimal surfaces
Time and place
1 PM on Thursday, November 29th, 2012; NAC 6/113
Christine Breiner (Columbia University)
Abstract
In a series of seminal papers, Colding and Minicozzi develop a compactness theory for sequences of non self-intersecting minimal disks without presuming any bounds on curvature or area. The helicoid had long been presumed to be the only unbounded, non self-intersecting minimal disk that was not a plane. The new compactness results gave further credence to this important conjecture, later proven by Meeks and Rosenberg with the help of this theory.
In this talk, I will begin by defining a minimal surface and providing both classical and non-classical examples. Next, I will briefly outline previously known results and explain how the Colding-Minicozzi theory relates to them. I will close by explaining three major breakthroughs that are consequences of this theory. One of these, my work joint with J. Bernstein, determines the global structure of any unbounded, non self-intersecting minimal surface with finite genus and one end.
