Some scalar curvature warped product splitting theorems

Gregory J. Galloway, Hyun Chul Jang

Research output: Contribution to journalArticle

Abstract

We present several rigidity results for Riemannian manifolds (M, g) with scalar curvature S ≥ −n(n − 1) (or S ≥ 0), and having compact boundary N satisfying a related mean curvature inequality. The proofs make use of results on marginally outer trapped surfaces applied to appropriate initial data sets. One of the results involves an analysis of Obata's equation on manifolds with boundary. This result is relevant to recent work of Lan-Hsuan Huang and the second author concerning the rigidity of asymptotically locally hyperbolic manifolds with zero mass.

Original languageEnglish (US)
Pages (from-to)2617-2629
Number of pages13
JournalProceedings of the American Mathematical Society
Volume148
Issue number6
DOIs
StatePublished - 2020

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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