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arxiv: 1310.3002 · v1 · submitted 2013-10-11 · 🧮 math.DG

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The Penrose inequality for asymptotically locally hyperbolic spaces with nonpositive mass

Dan A. Lee , Andr\'e Neves
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classification 🧮 math.DG
keywords massinequalitymetricsnegativepenroseasymptoticallycurvaturehyperbolic
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In the asymptotically locally hyperbolic setting it is possible to have metrics with scalar curvature at least -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. Chru\'sciel 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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Positivity of holographic energy

    gr-qc 2026-04 unverdicted novelty 6.0

    Positivity of a weighted holographic energy is proven for 4D spacetimes with negative cosmological constant and conformally static boundaries of spherical or toroidal topology with compatible spin structure.

  2. Positivity of holographic energy

    gr-qc 2026-04 unverdicted novelty 5.0

    Positivity is proven for a weighted holographic energy in 4D asymptotically AdS spacetimes with conformally static boundaries of spherical or toroidal topology.