Rigidity of entire graphs in weighted product spaces with nonnegative Bakry-Emery-Ricci tensor

被引：5
|
作者：
de Lima, Henrique F. [1 ]
Oliveira, Arlandson M. S. [1 ]
Santos, Marcio S. [2 ]
机构：
[1] Univ Fed Campina Grande, Dept Matemat, BR-58429970 Campina Grande, Paraiba, Brazil
[2] Univ Fed Alagoas, Inst Matemat, BR-57072970 Maceio, Alagoas, Brazil
来源：
ADVANCES IN GEOMETRY | 2017年 / 17卷 / 01期
关键词：
Weighted product spaces; Gaussian space; Bakry-Emery-Ricci tensor; drifting Laplacian; f-mean curvature; entire graphs; f-parabolic graphs; RIEMANNIAN-MANIFOLDS; THEOREM;
D O I：
10.1515/advgeom-2016-0024
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the rigidity of entire graphs defined over the fiber of a weighted product space whose Bakry-Emery-Ricci tensor is nonnegative. Supposing that the weighted mean curvature is constant and assuming appropriated constraints on the norm of the gradient of the smooth function u which determines such a graph Sigma(u), we prove that u is constant. Our proof is based on a formula for the Laplacian of an angle function attached to a hypersurface and on a weak version of the Omori-Yau generalized maximum principle.
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页码：53 / 59
页数：7
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