Rigidity of manifolds with boundary under a lower Ricci curvature bound

Yohei Sakurai

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arXiv · 1404.3845

Rigidity of manifolds with boundary under a lower Ricci curvature bound

Yohei Sakurai

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Abstract

We study Riemannian manifolds with boundary under a lower Ricci curvature bound, and a lower mean curvature bound for the boundary. We prove a volume comparison theorem of Bishop-Gromov type concerning the volumes of the metric neighborhoods of the boundaries. We conclude several rigidity theorems. As one of them, we obtain a volume growth rigidity theorem. We also show a splitting theorem of Cheeger-Gromoll type under the assumption of the existence of a single ray.

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Yohei Sakurai. 2014-04-15. Rigidity of manifolds with boundary under a lower Ricci curvature bound. https://arxiv.org/abs/1404.3845

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