紧流形上的第一特征值

数学季刊 ›› 2005, Vol. 20 ›› Issue (2): 200-205.

紧流形上的第一特征值

Department of Mathematics, Beihang University, Beijing 100083, China

收稿日期:2003-03-08 出版日期:2005-06-30 发布日期:2024-01-24
作者简介:ZHAO Di(1962-),male,native of Luoyang,Henan,Ph.D.,an associate professor of Beihang University,engages in differential geometry.
基金资助:
Supported by the NNSF of China(10271011) Supported by LIMB of the Ministry of Education China；

The First Eigenvalue of a Compact Manifold

Department of Mathematics, Beihang University, Beijing 100083, China

Received:2003-03-08 Online:2005-06-30 Published:2024-01-24
About author:ZHAO Di(1962-),male,native of Luoyang,Henan,Ph.D.,an associate professor of Beihang University,engages in differential geometry.
Supported by:
Supported by the NNSF of China(10271011) Supported by LIMB of the Ministry of Education China；

摘要/Abstract

摘要： This paper discusses the first eigenvalue on a compact Riemann manifold with the negative lower bound Ricci curvature. Let M be a compact Riemann manifold with the Ricci curvature≥-R, R=const.≥0 and d is the diameter of M. Our main result is that the first eigenvalue λ₁of M satisfies λ₁≥π²/d²-0.518.R.

关键词: Ricci , curvature;first , eigenvalue

Abstract: This paper discusses the first eigenvalue on a compact Riemann manifold with the negative lower bound Ricci curvature. Let M be a compact Riemann manifold with the Ricci curvature≥-R, R=const.≥0 and d is the diameter of M. Our main result is that the first eigenvalue λ₁of M satisfies λ₁≥π²/d²-0.518.R.

Key words: Ricci , curvature;first , eigenvalue

中图分类号:

O186.1

赵迪, 杨建安. 紧流形上的第一特征值[J]. 数学季刊, 2005, 20(2): 200-205.

ZHAO Di, YANG Jian-an. The First Eigenvalue of a Compact Manifold[J]. Chinese Quarterly Journal of Mathematics, 2005, 20(2): 200-205.

[1]	SARWAR Qanitah 黄振友 ZAHID Abdul Hannan. 具有勢壘的Sturm-Liouville算子的特徵值和特徵函數[J]. 数学季刊, 2023, 38(1): 50-61.
[2]	周后卿. 循环图的距离能量[J]. 数学季刊, 2018, 33(3): 233-239.
[3]	周后卿. 整循环图的秩[J]. 数学季刊, 2014, 29(1): 116-124.
[4]	张艳霞, 张学锋. 左定Sturm-Liouville问题的特征值不等式[J]. 数学季刊, 2010, 25(2): 300-307.
[5]	王鸿燕, 赵占锋, 亓正申. 一类并联冗余可修复系统解的线性稳定性[J]. 数学季刊, 2009, 24(3): 458-463.
[6]	饶若峰, 何庆高. 拟线性椭圆方程非零解[J]. 数学季刊, 2009, 24(1): 117-124.
[7]	谢强军, 张花荣, 唐旭华. 具有饱和项的捕食食饵系统正周期解的存在性[J]. 数学季刊, 2007, 22(2): 290-295.
[8]	徐森林, 宋冰玉. 具有非负Ricci曲率和大体积增长的开流形[J]. 数学季刊, 2006, 21(4): 475-481.
[9]	张建平, 蔡果兰. 一类脉冲微分方程边值问题的特征值[J]. 数学季刊, 2006, 21(3): 375-380.
[10]	田方. 强正则自补图的一个注记[J]. 数学季刊, 2006, 21(1): 62-65.
[11]	冯秀芳, 兰社云, 丁璐, 郑驻军. Spin^cDirac算子的特征值[J]. 数学季刊, 2004, 19(2): 120-125.
[12]	郭新伟 . 关于希尔伯特空间两球的高斯测度之差别的一个评注[J]. 数学季刊, 1999, 14(2): 47-51.
[13]	周振荣 . 关于超曲面第一特征值的一点注记[J]. 数学季刊, 1999, 14(2): 28-32.
[14]	江兆林, 叶留青, 邓方安. The Explicit Expressions of Level- k(r₁,r₂ ,… ,r_k) Circulant Matrices and Their Some Properties[J]. 数学季刊, 1998, 13(2): 91-96.
[15]	徐新生, 张洪武, 钟万勰. A Direct Method for the Problem of the Solid Cylinder in Elasticity[J]. 数学季刊, 1998, 13(1): 44-54.