| 高斯曲率估计及常数平均曲率超曲面的稳定性 |
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| 引用本文： | 李国明. 高斯曲率估计及常数平均曲率超曲面的稳定性[J]. 沈阳工业大学学报, 1995, 17(1): 88-93 |
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| 作者姓名： | 李国明 |
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| 作者单位： | 沈阳职工大学 |
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| 摘 要： | 利用活动标架法与Ｌａｐｌａｃｉａｎ特征值方法研究了具有常数平均曲率超曲面的稳定性问题。给出了三维拟常曲率流形中具有常数平均曲率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超曲而上的一个单连通有界区域为稳定的充分条件
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| 关 键 词： | 超曲面；特征值；稳定性 |
Gaussian Curvature Estimates and Stabillty ofHypersurfaces With Constant Nean Curvature |
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| Li Guoming. Gaussian Curvature Estimates and Stabillty ofHypersurfaces With Constant Nean Curvature[J]. Journal of Shenyang University of Technology, 1995, 17(1): 88-93 |
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| Authors: | Li Guoming |
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| Affiliation: | Shenyang Cellege for Staff and Worders |
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| Abstract: | In this paper, stabilities of hypersurfaces with constant mean curvature were studied bymeans of methods of moving frame and eigenvalues of the Laplacian. Some estimates ofGaussian curvature of conformal metric of 2-dimensional hypersurfaces with constant meancurvature immerged in 3-dimensional manifold of quasi-constant curvature were obtained.Sufficient conditions for a simply-connected domain of 2-dimensional hypersurfaces with cons-tant mean curvature immerged in 3-dimensional manifolds of quasi-constant cvrvature to bestable were proved. |
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| Keywords: | Riemannian geometry hypersurfaces stability characteristic value |
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