| ESTIMATE ON LOWER BOUND OF THE FIRST EIGENVALUE OF A COMPACT RIEMANNIAN MANIFOLD |
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| 作者姓名： | Cai Kairen |
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| 作者单位： | Department of |
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| 摘 要： | The author gives an optimum estimate of the first eigenvalue of a compact Riemannian manifold. It is shown that let M be a compact Riemannian manifold, then the first eigenvalue λ_1 of the Laplace operator of M satisfies α_1+max{0,-(n-1)K}≥π~2/d~2 where d is the diameter of M and (n-1)K is the negative lower bound of the Ricci curvature of M.
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| 收稿时间： | 1988/10/28 0:00:00 |
ESTIMATE ON LOWER BOUND OF THE FIRST EIGENVALUE OF A COMPACT RIEMANNIAN MANIFOLD |
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| Cai Kairen.ESTIMATE ON LOWER BOUND OF THE FIRST EIGENVALUE OF A COMPACT RIEMANNIAN MANIFOLD[J].Chinese Annals of Mathematics,Series B,1991,12(3):267-271. |
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| Authors: | Cai Kairen |
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| Institution: | Department of Mathematics,Hangzhou Teachers College,Hangzhou, Zhejiang, China. |
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| Abstract: | The author gives an optimum estimate of the first eigenvalue of a compact Riemannian manifold. It is shown that let M be a compact Riemannian manifold, then the first eigenvalue $\lambda_{1}$ of the Laplace operator of M satisfies $\lambda_{1}+ \max{0,-(n-1)K}\geq \pi^{2}/d^{2}$ where $d$ is the diameter of $M$ and $(n-1)K$ is the fegative lower bound of the Ricci curvature of $M$. |
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