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

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 $\hat{I}¸$-energy-minimizing half-cylinder, or, under certain topological assumptions, a $\hat{I}¸$-energy-minimizing strip for $\hat{I}¸\in (0,\ddot{I}€)$.

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