Rigidity of Riemannian Penrose inequality with corners and its implications

Siyuan Lu; Pengzi Miao

doi:10.1016/j.jfa.2021.109231

Rigidity of Riemannian Penrose inequality with corners and its implications

Siyuan Lu, Pengzi Miao

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Article number	109231
Journal	Journal of Functional Analysis
Volume	281
Issue number	10
DOIs	https://doi.org/10.1016/j.jfa.2021.109231
State	Published - Nov 15 2021

Keywords

Isometric embedding
Mean curvature
Scalar curvature

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2021.109231

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title = "Rigidity of Riemannian Penrose inequality with corners and its implications",

abstract = "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.",

keywords = "Isometric embedding, Mean curvature, Scalar curvature",

author = "Siyuan Lu and Pengzi Miao",

note = "Funding Information: Siyuan Lu acknowledges the support of NSERC Grant RGPIN-2020-06756 and DGECR-2020-00359 . Pengzi Miao acknowledges the support of NSF Grant DMS-1906423 . Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

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AU - Miao, Pengzi

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PY - 2021/11/15

Y1 - 2021/11/15

N2 - 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.

AB - 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.

KW - Isometric embedding

KW - Mean curvature

KW - Scalar curvature

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Rigidity of Riemannian Penrose inequality with corners and its implications

Abstract

Keywords

ASJC Scopus subject areas

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