New Calabi-Bernstein type results in weighted generalized Robertson-Walker spacetimes

被引：10
|
作者：
Cavalcante, M. P. [1 ]
de Lima, H. F. [2 ]
Santos, M. S. [1 ]
机构：
[1] Univ Fed Alagoas, Inst Matemat, BR-57072970 Maceio, Alagoas, Brazil
[2] Univ Fed Campina Grande, Dept Matemat, BR-58429970 Campina Grande, Paraiba, Brazil
来源：
ACTA MATHEMATICA HUNGARICA | 2015年 / 145卷 / 02期
关键词：
generalized Robertson-Walker spacetime; weighted manifold; Bakry-Emery Ricci tensor; drifting Laplacian; weighted mean curvature; complete spacelike hypersurface; COMPLETE SPACELIKE HYPERSURFACES; CONSTANT MEAN-CURVATURE; RIEMANNIAN-MANIFOLDS; GEOMETRY; UNIQUENESS;
D O I：
10.1007/s10474-014-0461-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We apply suitable generalized maximum principles in order to obtain new Calabi-Bernstein's type results concerning complete spacelike hypersurfaces immersed in a weighted generalized Robertson-Walker spacetime. Assuming a natural comparison inequality between the weighted mean curvatures of the hypersurface and those of the slices of the timelike bounded region where the hypersurface is supposed to be contained, we get sufficient conditions which guarantee that such a hypersurface must be a slice. Furthermore, we also treat the case when the ambient spacetime is static.
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页码：440 / 454
页数：15
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