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Rigidity of area minimizing tori in 3-manifolds of nonnegative scalar curvature

Mingliang Cai·Greg Galloway
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Abstract

The following version of a conjecture of Fischer-Colbrie and Schoen is proved: If M is a complete Riemannian 3-manifold with nonnegative scalar curvature which contains a two-sided torus S which is of least area in its isotopy class then M is flat. This follows from a local version derived in the paper.

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Mingliang Cai, Greg Galloway. 1999-06-01. Rigidity of area minimizing tori in 3-manifolds of nonnegative scalar curvature. https://arxiv.org/abs/math/9804096

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