Inverse mean curvature flow
Geometric flow / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Inverse mean curvature flow?
Summarize this article for a 10 year old
In the mathematical fields of differential geometry and geometric analysis, inverse mean curvature flow (IMCF) 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 (M, g) 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(t, ⋅).
If g is Riemannian, if S is closed with dim(M) = dim(S) + 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.[1]