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Large Isoperimetric Regions in Asymptotically Hyperbolic Manifolds

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Abstract

We show the existence of isoperimetric regions of sufficiently large volumes in general asymptotically hyperbolic three manifolds. Furthermore, we show that large coordinate spheres are uniquely isoperimetric in manifolds that are Schwarzschild–anti-deSitter at infinity. These results have important repercussions for our understanding of spacelike hypersurfaces in Lorentzian space-times which are asymptotic to null infinity. In fact, as an application of our results, we verify the asymptotically hyperbolic Penrose inequality in the special case of the existence of connected isoperimetric regions of all volumes.

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  1. Department of Mathematics, Stanford University, 450 Serra Mall, Bldg 380, Stanford, CA, 94305, USA

    Otis Chodosh

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  1. Otis Chodosh
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Correspondence to Otis Chodosh.

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Communicated by P. T. Chruściel

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Chodosh, O. Large Isoperimetric Regions in Asymptotically Hyperbolic Manifolds. Commun. Math. Phys. 343, 393–443 (2016). https://doi.org/10.1007/s00220-015-2457-y

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