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A nonlinear partial differential equation for the volume preserving mean curvature flow

We analyze the evolution of multi-dimensional normal graphs over 
the unit sphere under volume preserving mean curvature flow and 
derive a non-linear partial differential equation in polar 
coordinates. Furthermore, we construct finite difference numerical 
schemes and present numerical results for the evolution of 
non-convex closed plane curves under this flow, to observe that 
they become convex very fast.