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Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces

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Abstract

We establish versions of the positive mass and Penrose inequalities for a class of asymptotically hyperbolic hypersurfaces. In particular, under the usual dominant energy condition, we prove in all dimensions \(n\ge 3\) an optimal Penrose inequality for certain graphs in hyperbolic space \(\mathbb {H}^{n+1}\) whose boundary has constant mean curvature \(n-1\). This settles, for this class of manifolds, an inequality first conjectured by Wang (J Differ Geom 57(2):273–299, 2001).

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Acknowledgments

The authors would like to thank Fernando Marques for many enlightening conversations during the preparation of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Federal University of Ceará, Av. Humberto Monte, s/n, Campus do Pici, Bloco 914, Fortaleza, CE, 60455-760, Brazil

    Levi Lopes de Lima & Frederico Girão

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  1. Levi Lopes de Lima
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  2. Frederico Girão
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Correspondence to Frederico Girão.

Additional information

Levi Lopes de Lima was partially supported by CNPq/Brazil and FUNCAP/CE.

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de Lima, L.L., Girão, F. Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces. Gen Relativ Gravit 47, 23 (2015). https://doi.org/10.1007/s10714-015-1870-z

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