Stability of the surface area preserving mean curvature flow in   Euclidean space
  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 L^2-norm of the traceless second fundamental form is small (but the initial hypersurface is not necessarily convex). 
Zheng Huang and Longzhi Lin
math.DG math.AP