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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: http://hdl.handle.net/11858/00-001M-0000-0013-5581-4 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5583-F
Genre: Journal Article

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59-3-1.pdf (Publisher version), 605KB
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 Creators:
Huisken, Gerhard1, Author              
Ilmanen, Tom, Author
Affiliations:
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: 2001-11
 Publication Status: Published in print
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 Identifiers: eDoc: 332556
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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