正Ricci曲率的紧流形上第一特征值下界的新估计

数学物理学报 ›› 2016, Vol. 36 ›› Issue (2): 215-230.

正Ricci曲率的紧流形上第一特征值下界的新估计

何跃

南京师范大学数学科学学院数学研究所南京 210023

收稿日期:2015-09-01 修回日期:2016-01-03 出版日期:2016-04-25 发布日期:2016-04-25
作者简介:何跃,heyue@njnu.edu.cn,heyueyn@163.com
基金资助:
国家自然科学基金(11171158)和江苏高校优势学科建设工程资助项目资助

New Estimates of Lower Bound for the First Eigenvalue on Compact Manifolds with Positive Ricci Curvature

He Yue

Institute of Mathematics, School of Mathematics Sciences, Nanjing Normal University, Nanjing 210023

Received:2015-09-01 Revised:2016-01-03 Online:2016-04-25 Published:2016-04-25
Supported by:
Supported by the NSFC (11171158) and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions

摘要/Abstract

摘要：

将研究Ricci曲率以非负常数为下界的紧致黎曼流形上第一(闭的,Dirichlet,或Neumann)特征值下界,并给出第一特征值新的下界估计,以及Ling的估计^[16]一个容易的证明.虽然仍使用Ling的某些方法,但是该文的证明避免了试验函数奇性的产生,并且在很大程度上简化了Ling的计算,这或许提供了估计特征值的一种新方式.

关键词: 具有正Ricci曲率的紧致黎曼流形, Laplace算子, 第一特征值下界, 流形的直径, 流形的内切半径

Abstract:

In this paper we study the lower bound for the first (closed, or Dirichlet, or Neumann) eigenvalue of the Laplace operator on compact Riemannian manifolds with its Ricci curvature bounded below by nonnegative constant, and give a new estimate of lower bound for the first (closed, or Neumann) eigenvalue and also an easy proof of Ling's an estimate^[16]. Although we use Ling's methods on the whole, to some extent we deal with the singularity of test functions and greatly simplify many of the calculations involved. Maybe we provide a new way for estimating eigenvalues.

Key words: Compact Riemannian manifold with positive Ricci curvature, Laplace operator, Lower bounds for the first eigenvalue, Diameter of manifold, Inscribed radius of manifold

中图分类号:

O186.1

何跃. 正Ricci曲率的紧流形上第一特征值下界的新估计[J]. 数学物理学报, 2016, 36(2): 215-230.

He Yue. New Estimates of Lower Bound for the First Eigenvalue on Compact Manifolds with Positive Ricci Curvature[J]. Acta mathematica scientia,Series A, 2016, 36(2): 215-230.

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