ESTIMATE ON LOWER BOUND OF THE FIRST EIGENVALUE OF A COMPACT RIEMANNIAN MANIFOLD
Citation：
Cai Kairen.ESTIMATE ON LOWER BOUND OF THE FIRST EIGENVALUE OF A COMPACT RIEMANNIAN MANIFOLD[J].Chinese Annals of Mathematics B,1991,12(3):267~271
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Authors：
Cai Kairen;
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 $M$.
