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The Penrose Inequality for Asymptotically Locally Hyperbolic Spaces with Nonpositive Mass

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Abstract

In the asymptotically locally hyperbolic setting it is possible to have metrics with scalar curvature ≥ −6 and negative mass when the genus of the conformal boundary at infinity is positive. Using inverse mean curvature flow, we prove a Penrose inequality for these negative mass metrics. The motivation comes from a previous result of P. Chruściel and W. Simon, which states that the Penrose inequality we prove implies a static uniqueness theorem for negative mass Kottler metrics.

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Authors and Affiliations

  1. Queens College, New York, USA

    Dan A. Lee

  2. Imperial College, London, UK

    André Neves

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  1. Dan A. Lee
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  2. André Neves
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Correspondence to Dan A. Lee.

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Communicated by P. T. Chruściel

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Lee, D.A., Neves, A. The Penrose Inequality for Asymptotically Locally Hyperbolic Spaces with Nonpositive Mass. Commun. Math. Phys. 339, 327–352 (2015). https://doi.org/10.1007/s00220-015-2421-x

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  • DOI: https://doi.org/10.1007/s00220-015-2421-x

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