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In the mathematical fields of differential geometry and geometric analysis, inverse mean curvature flow is a geometric flow of submanifolds of a Riemannian or pseudo-Riemannian manifold. It has been used to prove a certain case of the Riemannian Penrose inequality, which is of interest in general relativity.
Formally, given a pseudo-Riemannian manifold and a smooth manifold S, an inverse mean curvature flow consists of an open interval I and a smooth map F from I × S into M such that
where H is the mean curvature vector of the immersion F.
If g is Riemannian, if S is closed with dim = dim + 1, and if a given smooth immersion f of S into M has mean curvature which is nowhere zero, then there exists a unique inverse mean curvature flow whose "initial data" is f.