Inverse mean curvature flow

Summary

Inverse mean curvature flow is a geometric evolution of hypersurfaces. Each point moves outward along the unit normal, with speed equal to the reciprocal of the mean curvature. It needs a hypersurface with positive mean curvature. Under this flow the area of the hypersurface grows exponentially in time. Huisken and Ilmanen used a weak form of this flow to prove the Riemannian Penrose inequality for a connected horizon.