A rigidity result for the graph case of the Penrose inequality
Differential Geometry
2021-07-30 v3 General Relativity and Quantum Cosmology
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).
Keywords
Cite
@article{arxiv.1205.1132,
title = {A rigidity result for the graph case of the Penrose inequality},
author = {Levi Lopes de Lima and Frederico Girão},
journal= {arXiv preprint arXiv:1205.1132},
year = {2021}
}
Comments
10 pages; abstract and introduction rewritten; minor corrections; references added; this posting has been superseded by arXiv:2107.03037, which handles the general pure Lovelock case