Time

Oct 21 2008 - 2:30pm

Location

CC 0248

Speaker

Mao-Pei Tsui (University of Toledo)

Abstract

Mean curvature flow is the heat equation for submanifolds. During this process, a submanifold evolves so as to decrease its area as fast as possible. The stationary points of mean curvature flow correspond to minimal submanifolds. In this talk, I will explain how to use mean curvature flow to deform a map between manifolds. We prove the global existence and convergence of the mean curvature flow of the graph of a map under various geometric conditions. A corollary is that any area-decreasing map between unit spheres (of possibly different dimensions) is homotopic to a constant map. This is joint work with Mu-Tao Wang.