Uniqueness of isometric immersions with the same mean curvature

Chunhe Li, Pengzi Miao, Zhizhang Wang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Motivated by the quasi-local mass problem in general relativity, we study the rigidity of isometric immersions with the same mean curvature into a warped product space. As a corollary of our main result, two star-shaped hypersurfaces in a spatial Schwarzschild or AdS-Schwarzschild manifold with nonzero mass differ only by a rotation if they are isometric and have the same mean curvature. We also prove similar results if the mean curvature condition is replaced by an σ2-curvature condition.

Original languageEnglish (US)
JournalJournal of Functional Analysis
DOIs
StateAccepted/In press - Jan 1 2018

Fingerprint

Isometric Immersion
Mean Curvature
Uniqueness
Warped Product
Product Space
General Relativity
Isometric
Rigidity
Hypersurface
Star
Corollary
Curvature

Keywords

  • Isometric embedding
  • Mean curvature
  • Quasi-local mass

ASJC Scopus subject areas

  • Analysis

Cite this

Uniqueness of isometric immersions with the same mean curvature. / Li, Chunhe; Miao, Pengzi; Wang, Zhizhang.

In: Journal of Functional Analysis, 01.01.2018.

Research output: Contribution to journalArticle

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