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  "body": "\n## Summary\n\nInverse mean curvature flow is a geometric evolution of hypersurfaces.\nEach point moves outward along the unit normal, with speed equal to the reciprocal of the [[mean curvature|PA78NFEPCF]].\nIt needs a hypersurface with positive mean curvature.\nUnder this flow the area of the hypersurface grows exponentially in time.\nHuisken and Ilmanen used a weak form of this flow to prove the Riemannian Penrose inequality for a connected horizon.\n\n## Explanations\n\n### L1 human\n\nThink of a closed surface that expands outward.\nWhere the surface is strongly curved it moves slowly, and where it is nearly flat it moves fast.\nThis is the opposite of mean curvature flow, where curved parts move fastest and the surface shrinks.\nA round sphere of radius $r$ in $\\R^3$ has mean curvature $2/r$ (with $H$ the sum of the principal curvatures), so it expands with speed $r/2$.\nIts radius is then $r_0 e^{t/2}$ at time $t$, and its area is $e^t$ times the initial area.\n",
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