Stable constant mean curvature hypersurfaces in some Riemannian manifolds

被引：16

作者：

Montiel, S ^{[1
]}

机构：

[1] Univ Granada, Dept Geometria & Topol, E-18071 Granada, Spain

来源：

COMMENTARII MATHEMATICI HELVETICI | 1998年 / 73卷 / 04期

关键词：

constant mean curvature; hypersurface; stability;

D O I：

10.1007/s000140050070

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine all stable constant mean curvature hypersurfaces in a wide class of complete Riemannian manifolds having a foliation whose leaves are umbilical hypersurfaces. Among the consequences of this analysis we obtain all the stable constant mean curvature hypersurfaces in many nonsimply connected hyperbolic space forms.

引用

页码：584 / 602

页数：19

共 22 条

[1]

Aleksandrov AD., 1956, VESTNIK LENINGRAD U, V11, P5

[2] STABILITY OF HYPERSURFACES WITH CONSTANT MEAN-CURVATURE [J].

BARBOSA, JL ;

DOCARMO, M .

MATHEMATISCHE ZEITSCHRIFT, 1984, 185 (03) :339-353

[3]

BARBOSA L, 1988, MATH Z, V197, P123

[4] MANIFOLDS OF NEGATIVE CURVATURE [J].

BISHOP, RL ;

ONEILL, B .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 145 :1-&

[5] INTEGRAL FORMULAS AND HYPERSPHERES IN A SIMPLY CONNECTED SPACE FORM [J].

BIVENS, I .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (01) :113-118

[6] ISOPERIMETRIC-INEQUALITIES ON MINIMAL SUBMANIFOLDS OF SPACE-FORMS [J].

CHOE, JY ;

GULLIVER, R .

MANUSCRIPTA MATHEMATICA, 1992, 77 (2-3) :169-189

[7] INCREASE IN THE 2ND EIGENVALUE OF A SCHRODINGER OPERATOR ON A COMPACT MANIFOLD AND APPLICATIONS [J].

ELSOUFI, A ;

ILIAS, S .

JOURNAL OF FUNCTIONAL ANALYSIS, 1992, 103 (02) :294-316

[8] EXTRINSIC UPPER-BOUNDS FOR GAMMA-1 [J].

HEINTZE, E .

MATHEMATISCHE ANNALEN, 1988, 280 (03) :389-402

[9]

Jellett J., 1853, J MATH PURE APPL, VXVIII, P163

[10]

Kanai M., 1983, Tokyo J. Math., V6, P143

← 1 2 3 →