Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 54, Number 1 (2017), 85-119.
Rigidity of manifolds with boundary under a lower Ricci curvature bound
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.
Osaka J. Math., Volume 54, Number 1 (2017), 85-119.
First available in Project Euclid: 3 March 2017
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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