Weakly trapped submanifolds immersed in generalized Robertson-Walker spacetimes

被引：4

作者：

Cunha, Antonio W. ^{[1
]}

de Lima, Henrique F. ^{[2
]}

Lima, Eraldo A., Jr. ^{[3
]}

Santos, Marcio S. ^{[3
]}

机构：

[1] Univ Fed Piaui, Dept Matemat, BR-64049550 Teresina, Piaui, Brazil

[2] Univ Fed Campina Grande, Dept Matemat, BR-58429970 Campina Grande, Paraiba, Brazil

[3] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 484卷 / 01期

关键词：

Generalized Robertson-Walker spacetimes; Spacelike submanifolds; Mean curvature vector field; Weakly trapped submanifolds; SPACELIKE HYPERSURFACES; MAXIMUM-PRINCIPLES; MEAN-CURVATURE; SURFACES; UNIQUENESS; FORMS;

D O I：

10.1016/j.jmaa.2019.123734

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We deal with codimension two weakly trapped submanifolds (that is, the mean curvature vector field is causal) immersed in a generalized Robertson-Walker (GRW) spacetime. Under suitable hypothesis, we are able to prove that such a spacelike submanifold is immersed into a slice of the ambient space. For this, we use three main core concepts: the well known generalized maximum principle of Omori and Yau, stochastic completeness and another appropriate maximum principle at infinity due to Yau. We also construct a nontrivial example of weakly trapped submanifold in the static GRW spacetime -R x H-2 x R, illustrating the importance of our results.(C) 2019 Elsevier Inc. All rights reserved.

引用

页数：13

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