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arXiv · 1804.01751

A splitting theorem for scalar curvature

Otis Chodosh·Michael Eichmair·Vlad Moraru
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Abstract

We show that a Riemannian $3$-manifold with non-negative 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.~Gromollhas been conjectured by D.~Fischer-Colbrie and R.~Schoen and by M.~Cai and G.~Galloway.

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Otis Chodosh, Michael Eichmair, Vlad Moraru. 2018-04-05. A splitting theorem for scalar curvature. https://doi.org/10.1002/cpa.21803

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