RIGIDITY OF MANIFOLDS WITH BOUNDARY UNDER A LOWER RICCI CURVATURE BOUND

被引：0

作者：

Sakurai, Yohei ^{[1
]}

机构：

[1] Univ Tsukuba, Grad Sch Pure & Appl Sci, Tennodai 1-1-1, Tsukuba, Ibaraki 3058577, Japan

来源：

OSAKA JOURNAL OF MATHEMATICS | 2017年 / 54卷 / 01期

关键词：

MEASURE CONTRACTION PROPERTY; COMPACT MANIFOLDS; 1ST EIGENVALUE; RIEMANNIAN MANIFOLD; COMPARISON THEOREM; LAPLACE OPERATOR; P-LAPLACIAN; SPACES; PRODUCTS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：85 / 119

页数：35

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