The inverse mean curvature flow and the Riemannian Penrose Inequality

Huisken, Gerhard; Ilmanen, Tom

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The inverse mean curvature flow and the Riemannian Penrose Inequality

Huisken, G., & Ilmanen, T. (2001). The inverse mean curvature flow and the Riemannian Penrose Inequality. Journal of Differential Geometry, 59(3), 353-437.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-5581-4 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-5583-F

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Huisken, Gerhard¹, Author
Ilmanen, Tom, Author

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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012

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Abstract: LetM 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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Dates: Date issued: 2001-11

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Title: Journal of Differential Geometry

Source Genre: Journal

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Pages: - Volume / Issue: 59 (3) Sequence Number: - Start / End Page: 353 - 437 Identifier: ISSN: 0022-040X