Osaka Journal of Mathematics

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.

Article information

Source
Osaka J. Math., Volume 54, Number 1 (2017), 85-119.

Dates
First available in Project Euclid: 3 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1488531786

Mathematical Reviews number (MathSciNet)
MR3619750

Zentralblatt MATH identifier
1383.53031

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 53C24: Rigidity results

Citation

Sakurai, Yohei. Rigidity of manifolds with boundary under a lower Ricci curvature bound. Osaka J. Math. 54 (2017), no. 1, 85--119. https://projecteuclid.org/euclid.ojm/1488531786


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