Uniqueness of isometric immersions with the same mean curvature

Chunhe Li, Pengzi Miao, Zhizhang Wang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 σ 2 -curvature condition.

Original languageEnglish (US)
Pages (from-to)2831-2855
Number of pages25
JournalJournal of Functional Analysis
Volume276
Issue number9
DOIs
StatePublished - May 1 2019

Keywords

  • Isometric embedding
  • Mean curvature
  • Quasi-local mass

ASJC Scopus subject areas

  • Analysis

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