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November, 2001 The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality
Gerhard Huisken, Tom Ilmanen
J. Differential Geom. 59(3): 353-437 (November, 2001). DOI: 10.4310/jdg/1090349447

Abstract

Let M be an asymptotically flat 3-manifold of nonnegative scalar curvature. The Riemannian Penrose Inequality states that the area of an outermost minimal surface N in M is bounded by the ADM mass m according to the formula |N| ≤ 16πm2. We develop a theory of weak solutions of the inverse mean curvature flow, and employ it to prove this inequality for each connected component of N using Geroch's monotonicity formula for the ADM mass. Our method also proves positivity of Bartnik's gravitational capacity by computing a positive lower bound for the mass purely in terms of local geometry.

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Gerhard Huisken. Tom Ilmanen. "The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality." J. Differential Geom. 59 (3) 353 - 437, November, 2001. https://doi.org/10.4310/jdg/1090349447

Information

Published: November, 2001
First available in Project Euclid: 20 July 2004

zbMATH: 1055.53052
MathSciNet: MR1916951
Digital Object Identifier: 10.4310/jdg/1090349447

Rights: Copyright © 2001 Lehigh University

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Vol.59 • No. 3 • November, 2001
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