三维拟常曲率流形中常数平均曲率超曲面的稳定性  

Stability of Hypersurfaces With Constant Mean Curvature of Manifold of Quasi-constant Curvatore

作　　者：李国明[1] 

机构地区：[1]沈阳职工大学

出　　处：《沈阳工业大学学报》1994年第4期100-107,共8页Journal of Shenyang University of Technology

摘　　要：利用活动标架法及Ｌａｐｌａｃｉａｎ的特征值方法研究了三维拟常曲率流形中的具有常数平均曲率的超曲面的稳定性，给出了三维拟常曲率流形中具有常数平均曲率的超曲面的共形度量的高斯曲率之上界估计。证明了三维拟常曲率流形中具有常数平均曲率的超曲面上的一个单连通区域为稳定的充分条件。In this paper,stabilities of hypersurfaces with constant mean curvature were studied bymeans of methods of moving and eigenvalues of Laplacian,Some estimates of Gaussiancurvature of conformal measure of hypersurfaces with constant mean curvature immergedin 3-dimensional manifold of quasi-constant curvature were obtained. Sufficient conditionsfor a simple- connected domain of hypersurfaces with constant mean curvature immergedin 3-dimensional manifold of quasi constant curvature to be stable were proved.

关 键 词：黎曼几何 超曲面 稳定性 特征值 

分 类 号：O186.16[理学—数学]