Mean curvature flow

Summary

Mean curvature flow is the evolution of a hypersurface in which each point moves with velocity equal to the mean curvature vector. It is the gradient flow of the area, so it decreases area as fast as possible. The equation for the moving surface is a nonlinear, weakly parabolic system. It plays for surfaces the role that the heat equation plays for functions. It is a close relative of the inverse mean curvature flow and of the Ricci flow.