Rigidity of manifolds with boundary under a lower Ricci curvature bound
Rigidity of manifolds with boundary under a lower Ricci curvature bound
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DOI：
10.18910/61890
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发表时间：
2014-04
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影响因子：
--
通讯作者：
Y. Sakurai
中科院分区：
文献类型：
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作者：
Y. Sakurai
本文研究了具有下Ricci曲率界和下平均曲率界的黎曼流形。证明了一个关于边界度量邻域体积的Bishop-Gromov型体积比较定理。得到了几个刚性定理。作为其中之一，我们得到了一个体积增长刚性定理。在单射线存在的假设下，我们还证明了Cheeger-Gromoll类型的分裂定理。
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.