Rigidity of manifolds with boundary under a lower Ricci curvature bound

2014/04/15 by Sakurai, Yohei
#53C20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1404.3845

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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