Mean Curvature Flows For Isoparametric Submanifolds

Isoparametric submanifolds in Euclidean spaces and spheres are submanifolds with constant pincipal curvatures. We will show that the mean curvature flows of such submanifolds behaves very well. They always converge in finite time to smooth submanifolds of lower dimension. This is a joint work with Chuu-Lian Terng.