The Penrose inequality for asymptotically locally hyperbolic spaces with nonpositive mass

2013/10/11 by Lee, Dan A., Neves, André · 2 citations
#53C20 #83C99 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1310.3002

Abstract

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. Chruściel and W. Simon, which states that the Penrose inequality we prove implies a static uniqueness theorem for negative mass Kottler metrics.

Cited by

• Some rigidity results for static three-manifolds with boundary and positive scalar curvature
• Mass Lower Bounds for Asymptotically Locally Flat Manifolds

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