A splitting theorem for manifolds with spectral nonnegative Ricci curvature and mean-convex boundary

Abstract

We prove a splitting theorem for a smooth noncompact manifold with (possibly noncompact) boundary. We show that if a noncompact manifold of dimension $n\ge 2$ has $\hat{I}{»}_1(-\hat{I}\pm \hat{I}”+\mathrm{Ric})\ge 0$ for some $\hat{I}\pm <\frac{4}{n-1}$ and mean-convex boundary, then it is either isometric to $\hat{I}\pounds \times {\mathbb{R}}_{\ge 0}$ for a closed manifold $\hat{I}\pounds$ with nonnegative Ricci curvature or it has no interior ends.

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