Rigidity of Riemannian Penrose inequality with corners and its implications
Rigidity of Riemannian Penrose inequality with corners and its implications
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DOI：
10.1016/j.jfa.2021.109231
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发表时间：
2020-10
期刊：
影响因子：
--
通讯作者：
Siyuan Lu;P. Miao
中科院分区：
文献类型：
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作者：
Siyuan Lu;P. Miao
我们研究了在黎曼彭罗斯不等式中获得最优值的合适奇异度量。更准确地说，我们证明奇异度量在正确指定的坐标中必然是平滑的。当应用于空间史瓦西流形中包围视界的超曲面时，结果给出具有相同平均曲率的等距超曲面的刚性。
We study suitable singular metrics attaining the optimal value in the Riemannian Penrose inequality. More precisely, we demonstrate that the singular metric is necessarily smooth in properly specified coordinates. When applied to hypersurfaces enclosing the horizon in a spatial Schwarzschild manifold, the result gives the rigidity of isometric hypersurfaces with the same mean curvature.