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

共 32 条

[1] Stability and geometric properties of constant weighted mean curvature hypersurfaces in gradient Ricci solitons
Alencar, Hilario
Rocha, Adina
[J]. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2018, 53 (04) : 561 - 581
[2] A maximum principle at infinity with applications to geometric vector fields
Alias, L. J.
Caminha, A.
do Nascimento, F. Y.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 474 (01) : 242 - 247
[3] A maximum principle related to volume growth and applications
Alias, Luis J.
Caminha, Antonio
do Nascimento, F. Yure
[J]. ANNALI DI MATEMATICA PURA ED APPLICATA, 2021, 200 (04) : 1637 - 1650
[4] Bakry D., 1985, SEMINAIRE PROBABILIT, V1123, P177, DOI DOI 10.1007/BFB0075847
[5] Spectral and stochastic properties of the f-Laplacian, solutions of PDEs at infinity and geometric applications
Bessa, G. Pacelli
Pigola, Stefano
Setti, Alberto
[J]. REVISTA MATEMATICA IBEROAMERICANA, 2013, 29 (02) : 579 - 610
[6] Complete Vertical Graphs with Constant Mean Curvature in Semi-Riemannian Warped Products
Caminha, A.
de Lima, H. F.
[J]. BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2009, 16 (01) : 91 - 105
[7] Cao HD, 2010, J DIFFER GEOM, V85, P175
[8] Halfspace type theorems for self-shrinkers
Cavalcante, Marcos P.
Espinar, Jose M.
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2016, 48 : 242 - 250
[9] Rigidity of self-shrinkers and translating solitons of mean curvature flows
Chen, Qun
Qiu, Hongbing
[J]. ADVANCES IN MATHEMATICS, 2016, 294 : 517 - 531
[10] Cheng QM, 2018, CALC VAR PARTIAL DIF, V57, DOI 10.1007/s00526-018-1303-4

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