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  "body": "\n## Summary\n\nMean curvature flow is the evolution of a hypersurface in which each point moves with velocity equal to the mean curvature vector.\nIt is the gradient flow of the area, so it decreases area as fast as possible.\nThe equation for the moving surface is a nonlinear, weakly parabolic system.\nIt plays for surfaces the role that the [[heat equation|VP2HN86VAG]] plays for functions.\nIt is a close relative of the [[inverse mean curvature flow|5XVEF5DKAG]] and of the [[Ricci flow|CR14D9YQTY]].\n\n## Explanations\n\n### L1 human\n\nImagine a soap film or a closed curve that tries to shorten itself.\nEach point moves toward the inside of the bend, faster where the surface is more bent, as measured by its [[mean curvature|PA78NFEPCF]].\nA round sphere of radius $R_0$ in $\\R^{n+1}$ stays round and its radius shrinks as $\\sqrt{R_0^2 - 2nt}$.\nFor curves in the plane the flow is called curve shortening flow, and every embedded closed curve becomes round before it shrinks to a point.\n",
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