15 May 2009 On the Riemannian Penrose inequality in dimensions less than eight
Hubert L. Bray, Dan A. Lee
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Duke Math. J. 148(1): 81-106 (15 May 2009). DOI: 10.1215/00127094-2009-020


The positive mass theorem states that a complete asymptotically flat manifold of nonnegative scalar curvature has nonnegative mass and that equality is achieved only for the Euclidean metric. The Riemannian Penrose inequality provides a sharp lower bound for the mass when black holes are present. More precisely, this lower bound is given in terms of the area of an outermost minimal hypersurface, and equality is achieved only for Schwarzschild metrics. The Riemannian Penrose inequality was first proved in three dimensions in 1997 by G. Huisken and T. Ilmanen for the case of a single black hole (see [HI]). In 1999, Bray extended this result to the general case of multiple black holes using a different technique (see [Br]). In this article, we extend the technique of [Br] to dimensions less than eight. Part of the argument is contained in a companion article by Lee [L]. The equality case of the theorem requires the added assumption that the manifold be spin


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Hubert L. Bray. Dan A. Lee. "On the Riemannian Penrose inequality in dimensions less than eight." Duke Math. J. 148 (1) 81 - 106, 15 May 2009. https://doi.org/10.1215/00127094-2009-020


Published: 15 May 2009
First available in Project Euclid: 22 April 2009

zbMATH: 1168.53016
MathSciNet: MR2515101
Digital Object Identifier: 10.1215/00127094-2009-020

Primary: 53C20
Secondary: 83C57

Rights: Copyright © 2009 Duke University Press


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Vol.148 • No. 1 • 15 May 2009
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