SOME SCALAR CURVATURE WARPED PRODUCT SPLITTING THEOREMS

被引：3
|
作者：
Galloway, Gregory J. [1 ]
Jang, Hyun Chul [2 ]
机构：
[1] Univ Miami, Dept Math, Coral Gables, FL 33146 USA
[2] Univ Connecticut, Dept Math, Storrs, CT 06269 USA
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2020年 / 148卷 / 06期
关键词：
MINIMAL-SURFACES; TRAPPED SURFACES; RIGIDITY; MASS; 3-MANIFOLDS; MANIFOLDS; TOPOLOGY; EXISTENCE; PROOF;
D O I：
10.1090/proc/14922
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present several rigidity results for Riemannian manifolds (M, g) with scalar curvature S >= - n(n - 1) (or S >= 0), and having compact boundary N satisfying a related mean curvature inequality. The proofs make use of results on marginally outer trapped surfaces applied to appropriate initial data sets. One of the results involves an analysis of Obata's equation on manifolds with boundary. This result is relevant to recent work of Lan-Hsuan Huang and the second author concerning the rigidity of asymptotically locally hyperbolic manifolds with zero mass.
引用
收藏
页码：2617 / 2629
页数：13
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