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A rigidity result for the graph case of the Penrose inequality

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arxiv 1205.1132 v3 pith:J52CLFRJ submitted 2012-05-05 math.DG gr-qc

Levi Lopes de Lima , Frederico Girão This is my paper · ORCID
classification math.DGgr-qc
keywords resultrigidityeuclideanflatpenroseasymptoticallycasecondition
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In this note we prove a global rigidity result for asymptotically flat, scalar flat Euclidean hypersurfaces with a minimal horizon lying in a hyperplane, under a natural ellipticity condition. As a consequence we obtain, in the context of the Riemannian Penrose conjecture, a local rigidity result for the family of exterior Schwarzschild solutions (viewed as graphs in Euclidean space).

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