Rigidity of Riemannian Penrose inequality with corners and its implications
Differential Geometry
2020-10-19 v1 General Relativity and Quantum Cosmology
Analysis of PDEs
Abstract
Motivated by the rigidity case in the localized Riemannian Penrose inequality, we show that suitable singular metrics attaining the optimal value in the Riemannian Penrose inequality is necessarily smooth in properly specified coordinates. If applied to hypersurfaces enclosing the horizon in a spatial Schwarzschild manifold, the result gives the rigidity of isometric hypersurfaces with the same mean curvature.
Keywords
Cite
@article{arxiv.2010.07963,
title = {Rigidity of Riemannian Penrose inequality with corners and its implications},
author = {Siyuan Lu and Pengzi Miao},
journal= {arXiv preprint arXiv:2010.07963},
year = {2020}
}