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正Ricci曲率的紧流形上第一特征值下界的新估计
  • ISSN号：1003-3998
  • 期刊名称：《数学物理学报：A辑》
  • 时间：0
  • 分类：O186.1[理学—数学;理学—基础数学]
  • 作者机构：南京师范大学数学科学学院数学研究所,南京210023
  • 相关基金：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
作者： 何跃
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, Compact Riemannian manifold with positive Ricci curvature, Laplace operator, Lower bounds for the first eigenvalue, Diameter of manifold, Inscribed radius of manifold
中文摘要：

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.

英文摘要：

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.

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地球流体力学和物理学中一些非线性偏微分方程研究
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期刊信息
  • 《数学物理学报：A辑》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学院
  • 主办单位:中国科学院武汉物理与数学研究所
  • 主编：李邦河 陈贵强 朱熹平
  • 地址：湖北省武汉市武昌小洪山西路30号武汉71010信箱
  • 邮编：430071
  • 邮箱：actams@wipm.ac.cn
  • 电话：027-87199206
  • 国际标准刊号：ISSN：1003-3998
  • 国内统一刊号：ISSN：42-1226/O
  • 邮发代号:38-214
  • 获奖情况:
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  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:5382