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January 2017 Rigidity of manifolds with boundary under a lower Ricci curvature bound
Yohei Sakurai
Osaka J. Math. 54(1): 85-119 (January 2017).

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. "Rigidity of manifolds with boundary under a lower Ricci curvature bound." Osaka J. Math. 54 (1) 85 - 119, January 2017.

Information

Published: January 2017
First available in Project Euclid: 3 March 2017

zbMATH: 1383.53031
MathSciNet: MR3619750

Subjects:
Primary: 53C20
Secondary: 53C23, 53C24

Rights: Copyright © 2017 Osaka University and Osaka City University, Departments of Mathematics

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Vol.54 • No. 1 • January 2017
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