Glimpses of Mathematics, Now and Then: A Celebration of Karen Uhlenbeck's 80th birthday

Abstract: The existence theory of Sacks and Uhlenbeck opened up the possibility of using minimal two spheres to study geometric properties of manifolds. The other ingredient in this study is an understanding of the second variation of area. While there have been several successes in this study there are still many open questions about stable minimal surfaces in both flat space and Riemannian manifolds. This talk will survey some of the known results and describe some new ideas for surfaces which are stable and also have stable covering surfaces.