A Splitting Theorem for Scalar Curvature

Otis Chodosh, Michael Eichmair, Vlad Moraru

Research output: Contribution to journalArticle

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 1 2019

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Scalar Curvature
Nonnegative Curvature
Theorem
Analogue

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Mathematics(all)

Cite this

Chodosh, Otis ; Eichmair, Michael ; Moraru, Vlad. / A Splitting Theorem for Scalar Curvature. In: Communications on Pure and Applied Mathematics. 2019 ; Vol. 72, No. 6. pp. 1231-1242.
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A Splitting Theorem for Scalar Curvature. / Chodosh, Otis; Eichmair, Michael; Moraru, Vlad.

In: Communications on Pure and Applied Mathematics, Vol. 72, No. 6, 01.06.2019, p. 1231-1242.

Research output: Contribution to journalArticle

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