Rigidity of Riemannian Penrose inequality with corners and its implications

Siyuan Lu, Pengzi Miao

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Article number109231
JournalJournal of Functional Analysis
Volume281
Issue number10
DOIs
StatePublished - Nov 15 2021

Keywords

  • Isometric embedding
  • Mean curvature
  • Scalar curvature

ASJC Scopus subject areas

  • Analysis

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