| A LOWER BOUND FOR FIRST EIGENVALUE WITH MIXED BOUNDARY CONDITIOIN |
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| 引用本文： | RenXin′an XuHongwei. A LOWER BOUND FOR FIRST EIGENVALUE WITH MIXED BOUNDARY CONDITIOIN[J]. 高校应用数学学报(英文版), 2004, 19(2): 223-228. DOI: 10.1007/s11766-004-0057-2 |
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| 作者姓名： | RenXin′an XuHongwei |
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| 作者单位： | CenterofMathematicalSciences,ZhejiangUniversity,Hangzhou310027,China |
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| 摘 要： | Let M be an n-dimensional compact Riemannian manifold with or without boundary,and its Ricci curvature RicM≥n- 1. The paper obtains an inequality for the first eigenvalue η1 of M with mixed boundary condition, which is a generalization of the results of Lichnerowicz,Reilly, Escobar and Xia. It is also proved that η1≥ n for certain n-dimensional compact Riemannian manifolds with boundary,which is an extension of the work of Cheng,Li and Yau.
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| 关 键 词： | 特征值 黎曼几何 不等式 边界条件 N维空间 |
| 收稿时间： | 2004-01-09 |
A lower bound for first eigenvalue with mixed boundary condition |
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| Ren Xin’an,Xu Hongwei. A lower bound for first eigenvalue with mixed boundary condition[J]. Applied Mathematics A Journal of Chinese Universities, 2004, 19(2): 223-228. DOI: 10.1007/s11766-004-0057-2 |
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| Authors: | Ren Xin’an Xu Hongwei |
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| Affiliation: | (1) Center of Mathematical Sciences, Zhejiang University, 310027 Hangzhou, China |
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| Abstract: | Let M be an n-dimensional compact Riemannian manifold with or without boundary, and its Ricci curvature Ric M⩾n−1. The paper obtains an inequality for the first eigenvalue η 1 of M with mixed boundary condition, which is a generalization of the results of Lichnerowicz, Reilly, Escobar and Xia. It is also proved that η 1⩾n for certain n-dimensional compact Riemannian manifolds with boundary, which is an extension of the work of Cheng, Li and Yau. Research supported by the National Natural Science Foundation of China (10231010), Trans-Century Training Programme Foundation for Talents by the Ministry of Education of China, Natural Science Foundation of Zhejiang province. |
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| Keywords: | 58C40 53C20 |
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