紧致黎曼流形的第一特征值

Estiamtes of the first eigenvalue of a compact Riemannian manifold

本文证明了紧致黎曼流形Ｍ的Ｌａｐｌａｃｅ算子的第一特征值λ_１≥Ｋ，其中Ｋ＝ｍａｘ｛０，Ｒ｝，－Ｒ是Ｍ的Ｒｉｃｃｉ曲率的下界，ｄ是Ｍ的直径，这个估计改进了一些作者的最近结果，从而给出了第一特征值下界的最佳估计。

We prove that if M be a compact Riemannian manifold,then the first eigenvalue λ_l of the Laplacian of M satisfies λ_1≥K, where K＝max {0,R}, ─R is the lower bound of the Ricci curvature of M and d is the diameter of M. This estimate improves the recent results of some authors.