Compact Stable Constant Mean Curvature Surfaces in Homogeneous 3-manifolds

被引：16

作者：

Torralbo, Francisco ^{[1
]}

Urbano, Francisco ^{[1
]}

机构：

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

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2012年 / 61卷 / 03期

关键词：

homogeneous manifolds; constant mean curvature surfaces; stability; isoperimetric problem; COMPLEX PROJECTIVE-SPACE; S-2 X R; REAL HYPERSURFACES; STABILITY;

D O I：

10.1512/iumj.2012.61.4667

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify the stable constant mean curvature spheres in the homogeneous Riemannian 3-manifolds: the Berger spheres, the special linear group, and the Heisenberg group. We show that all of them are stable in the last two cases, while in some Berger spheres there are unstable ones. Also, we classify the stable compact orientable constant mean curvature surfaces in a certain subfamily of the Berger spheres. This allows us to solve the isoperimetric problem in some Berger spheres.

引用

页码：1129 / 1156

页数：28

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