Title: Stability and structure of minimal hypersurfaces Abstract: In this talk, a general method will be discussed in the use of studying the structure of complete stable minimal hypersurfaces (or more generally minimal hypersurfaces with finite index) in a complete Riemannian manifold with nonnegative curvature. Some historical perspective will be given. I will also demonstrate how one can use this method to recover previously known theorems as well as proving new results, hence putting the theory into one unified framework. Peter *************************************** Peter Li, Ph.D. Chancellor's Professor Department of Mathematics University of California, Irvine CA 92697-3875 USA 949-824-7049 949-824-7993 (fax) http://math.uci.edu/~pli