The Penrose Inequality for Asymptotically Locally Hyperbolic Spaces with Nonpositive Mass
By Dan A. Lee, A. Neves. 2013
74 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/8e288ba7ce0fdb5643a97add84356fd65703d219
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- On static three-manifolds with positive scalar curvature (2015, background): “The literature on the subject is extensive and many classification results are known particularly in the zero and negative scalar curvature cases (for example, see [35], [49], [54], [18], [4], [47], [25] and [12], [60], [52], [5], [26], [20], [41], [27]).”