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.

引用

页码：53 / 59

页数：7

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