The inverse mean curvature flow and the Riemannian Penrose inequality
Gerhard Huisken and Tom Ilmanen
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Submission date: 30. Apr. 1998
published in: Journal of differential geometry, 59 (2001) 3, p. 353-437
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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 , 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.