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arXiv · 2501.08677

A splitting theorem for 3-manifold with nonnegative scalar curvature and mean-convex boundary

Han Hong·Gaoming Wang
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Abstract

We show that a Riemannian 3-manifold with nonnegative scalar curvature and mean-convex boundary is flat if it contains an absolutely area-minimizing (in the free boundary sense) half-cylinder or strip. Analogous results also hold for a $\theta$-energy-minimizing half-cylinder, or, under certain topological assumptions, a $\theta$-energy-minimizing strip for $\theta\in (0,\pi)$.

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Han Hong, Gaoming Wang. 2025-01-15. A splitting theorem for 3-manifold with nonnegative scalar curvature and mean-convex boundary. https://arxiv.org/abs/2501.08677

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