A rigidity result for the graph case of the Penrose inequality

Abstract

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).

10 pages; abstract and introduction rewritten; minor corrections; references added; this posting has been superseded by arXiv:2107.03037, which handles the general pure Lovelock case

References in corpus (1)

• Positive mass and Penrose type inequalities for asymptotically hyperbolic hypersurfaces

Cited by in corpus (6)

• The Gauss-Bonnet-Chern mass for graphic manifolds
• A new mass for asymptotically flat manifolds
• A Penrose inequality for asymptotically locally hyperbolic graphs
• The equality case of the Penrose inequality for asymptotically flat graphs
• Penrose inequalities and a positive mass theorem for charged black holes in higher dimension
• Extrinsic black hole uniqueness in pure Lovelock gravity