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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
16/1998

The inverse mean curvature flow and the Riemannian Penrose inequality

Gerhard Huisken and Tom Ilmanen

Abstract

The Penrose conjecture of general relativity, in its purely Riemannian case, states the following: in an asymptotically flat 3-manifold of nonnegative scalar curvature, the area of each outermost minimal surface is bounded by $16\pi m^2$, where $m$ is the ADM mass associated to the infinite region. We develop a weak existence and uniqueness theory of the inverse mean curvature flow put forward by Geroch and Jang-Wald, and use it to prove this inequality, although the evolving surfaces jump around in the manifold. A corollary is the positive mass theorem of Schoen and Yau.

Received:
30.04.98
Published:
30.04.98

Related publications

inJournal
2001 Repository Open Access
Gerhard Huisken and Tom Ilmanen

The inverse mean curvature flow and the Riemannian Penrose inequality

In: Journal of differential geometry, 59 (2001) 3, pp. 353-437