Deforming Convex Hypersurfaces by Curvature Functions
We study the motion of any smooth, closed and uniformly convex hypersurface in R contracting along its normal vectorfield with the speed given by some suitable smooth, positive and symmetric function of the principal curvatures, including any power of the m-th mean curvature. We prove that the surface remains uniformly convex for a finite time interval and then shrinks to a single point. No pinching condition is needed in the discussion. AMS Classification Number: 35K55, 53A05.