A Splitting Theorem for Scalar Curvature

Otis Chodosh, Michael Eichmair, Vlad Moraru

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We show that a Riemannian 3-manifold with nonnegative scalar curvature is flat if it contains an area-minimizing cylinder. This scalar-curvature analogue of the classical splitting theorem of J. Cheeger and D. Gromoll (1971) was conjectured by D. Fischer-Colbrie and R. Schoen (1980) and by M. Cai and G. Galloway (2000).

Original languageEnglish (US)
Pages (from-to)1231-1242
Number of pages12
JournalCommunications on Pure and Applied Mathematics
Volume72
Issue number6
DOIs
StatePublished - Jun 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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