A Note on Constant Mean Curvature Foliations of Noncompact Riemannian Manifolds

被引：0

作者：

Ilias, S. ^{[1
]}

Nelli, B. ^{[2
]}

Soret, M. ^{[1
]}

机构：

[1] Univ Tours, Tours, France

[2] Univ LAquila, Laquila, Italy

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES | 2022年 / 2022卷

关键词：

HYPERSURFACES; SURFACES; INEQUALITIES; SPECTRUM;

D O I：

10.1155/2022/7350345

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We aimed to study constant mean curvature foliations of noncompact Riemannian manifolds, satisfying some geometric constraints. As a byproduct, we answer a question by M. P. do Carmo (see Introduction) about the leaves of such foliations.

引用

页数：4

共 18 条

[1] FOLIATIONS BY HYPERSURFACES WITH CONSTANT MEAN-CURVATURE
BARBOSA, JLM
KENMOTSU, K
OSHIKIRI, G
[J]. MATHEMATISCHE ZEITSCHRIFT, 1991, 207 (01) : 97 - 108
[2] ON THE SPECTRUM OF NON-COMPACT MANIFOLDS WITH FINITE VOLUME
BROOKS, R
[J]. MATHEMATISCHE ZEITSCHRIFT, 1984, 187 (03) : 425 - 432
[3] BROOKS R, 1981, P AM MATH SOC, V82, P473
[4] Cheeger J., 1970, PROBLEMS ANAL, V625, P110
[5] DIFFERENTIAL EQUATIONS ON RIEMANNIAN MANIFOLDS AND THEIR GEOMETRIC APPLICATIONS
CHENG, SY
YAU, ST
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1975, 28 (03) : 333 - 354
[6] On constant mean curvature hypersurfaces with finite index
Cheng, X
[J]. ARCHIV DER MATHEMATIK, 2006, 86 (04) : 365 - 374
[7] The structure of weakly stable constant mean curvature hypersurfaces
Cheng, Xu
Cheung, Leung-Fu
Zhou, Detang
[J]. TOHOKU MATHEMATICAL JOURNAL, 2008, 60 (01) : 101 - 121
[8] STABILITY OF COMPLETE NONCOMPACT SURFACES WITH CONSTANT MEAN-CURVATURE
DASILVEIRA, AM
[J]. MATHEMATISCHE ANNALEN, 1987, 277 (04) : 629 - 638
[9] Do Carmo M, 1998, LECT NOTES MATH, V1410, P133
[10] Stable constant mean curvature hypersurfaces
Elbert, Maria Fernanda
Nelli, Barbara
Rosenberg, Harold
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (10) : 3359 - 3366

← 1 2 →