UC Santa Cruz

The surface area preserving mean curvature flow is a mean curvaturetype flow with a global forcing term to keep the hypersurface areafixed. By iteration techniques, we show that the surface area preservingmean curvature flow in Euclidean space exists for all time and convergesexponentially to a round sphere, if initially the L2-norm of the traceless second fundamental form is small (but the initial hypersurface is notnecessarily convex).