Abstract
The surface area preserving mean curvature flow is a mean curvature type flow with a global forcing term to keep the hypersurface area fixed. By iteration techniques, we show that the surface area preserving mean curvature flow in Euclidean space exists for all time and converges exponentially to a round sphere, if initially the L2-norm of the traceless second fundamental form is small (but the initial hypersurface is not necessarily convex).
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