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.
Original language | English |
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Pages (from-to) | 85-119 |
Number of pages | 35 |
Journal | Osaka Journal of Mathematics |
Volume | 54 |
Issue number | 1 |
Publication status | Published - 2017 Jan |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)