A splitting theorem for scalar curvature
Differential Geometry
2019-09-05 v1
Abstract
We show that a Riemannian -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.
Keywords
Cite
@article{arxiv.1804.01751,
title = {A splitting theorem for scalar curvature},
author = {Otis Chodosh and Michael Eichmair and Vlad Moraru},
journal= {arXiv preprint arXiv:1804.01751},
year = {2019}
}
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