Uniqueness of hypersurfaces in weighted product spaces via maximum principles for the drift Laplacian

被引：0

作者：

da Silva, Danilo F. ^{[1
]}

Lima, Eraldo A., Jr. ^{[1
]}

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

机构：

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

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

来源：

BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA | 2023年 / 16卷 / 03期

关键词：

Weighted product spaces; Drift Laplacian; Bakry-emery-Ricci tensor; Shrinking Ricci solitons; Complete two-sided hypersurfaces; f-mean curvature; Bernstein type results; RIGIDITY THEOREMS; MEAN-CURVATURE; SELF-SHRINKERS; RICCI; STABILITY; GRAPHS; GAP;

D O I：

10.1007/s40574-022-00337-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We apply suitable maximum principles for the drift Laplacian to obtain several uniqueness results concerning complete two-sided hypersurfaces immersed with constant f-mean curvature in a weighted product space of form R x M-f(n) and such that its potential function f does not depend on the parameter t is an element of R. Among these results, we prove that the slices are the only complete two-sided f-minimal hypersurfaces lying in a half-space of R x M-f(n) and such that the Bakry-Emeri-Ricci tensor is bounded from below. Furthermore, we study the f-mean curvature equation related to entire graphs defined on the base M-n.

引用

页码：507 / 520

页数：14