A Splitting Theorem for Scalar Curvature

Otis Chodosh; Michael Eichmair; Vlad Moraru

doi:10.1002/cpa.21803

A Splitting Theorem for Scalar Curvature

Otis Chodosh, Michael Eichmair, Vlad Moraru

Research output: Contribution to journal › Article › peer-review

10 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 language	English (US)
Pages (from-to)	1231-1242
Number of pages	12
Journal	Communications on Pure and Applied Mathematics
Volume	72
Issue number	6
DOIs	https://doi.org/10.1002/cpa.21803
State	Published - Jun 2019

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1002/cpa.21803

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title = "A Splitting Theorem for Scalar Curvature",

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).",

author = "Otis Chodosh and Michael Eichmair and Vlad Moraru",

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AU - Eichmair, Michael

AU - Moraru, Vlad

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N2 - 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).

AB - 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).

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M3 - Article

AN - SCOPUS:85058497029

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EP - 1242

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

IS - 6

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A Splitting Theorem for Scalar Curvature

Abstract

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