Lower Bound of the First Eigenvalue for the Laplace Operator on Compact Riemannian Manifold
Lower Bound of the First Eigenvalue for the Laplace Operator on Compact Riemannian Manifold作者机构:Dep. of Mathematics Jiaozuo Mining Institute Henan China 454159
出 版 物:《Chinese Quarterly Journal of Mathematics》 (数学季刊(英文版))
年 卷 期:1993年第8卷第2期
页 面:40-49页
核心收录:
学科分类:07[理学] 070104[理学-应用数学] 0701[理学-数学]
基 金:其它基金
主 题:下界 第一特征值 Laplace算子 紧黎曼流形 Ricli曲率 梯度估计
摘 要:Let M be a compact m-dimensional Riemannian manifold,let d denote its diameter,-R(R0) the lower bound of the Ricci curvature,and λ1 the first eigenvalue for the Laplacian on *** there ex-ists a constant Cm=max{√m-1,√2},such that λ1≥π^2/d^2·1/(2-11/2π^2)+11/2π^2e^Cm√Rd^2.