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

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  • 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.
    Mathematics Subject Classification: Primary: 35; Secondary: 37.

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