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

祁锋;郭白妮

【期刊名称】《数学季刊：英文版》 【年(卷),期】1993(008)002

【摘要】Let M be a compact m-dimensional Riemannian manifold,let d denote its diameter,-R(R>0) the lower bound of the Ricci curvature,and λ1 the first eigenvalue for the Laplacian on M.Then there ex-ists a constant

Cm=max｛√m-1,√2｝,such

that

λ1≥π2/d2·1/(2-

11/2π2)+11/2π2eCm√Rd2. 【总页数】10页(40-49)

【关键词】下界;第一特征值;Laplace算子;紧黎曼流形;Ricli曲率;梯度估计 【作者】祁锋;郭白妮 【

作

者

单

位

】

Dep.ofMathematics,JiaozuoMiningInstitute,Henan.China,454159;Dep.ofMathematics,JiaozuoMiningInstitute,Henan.China,454159 【正文语种】英文 【中图分类】O177.6 【相关文献】

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