紧致Riemann流形第一特征值估计

紧致Riemann流形第一特征值估计

论文摘要

本综述报告综述了紧致Riemann流形上Laplace算子△的第一特征值的下界估计的历史,其中对一些定理与结论,报告作了证明与解析。

论文目录

  • 摘要
  • Abstract
  • 第一章 △的特征值
  • 1.1 基本概念与定理
  • 1.2 特征值问题
  • 第二章 紧致黎曼流形第一特征值下界估计
  • 2.1 紧致黎曼流形第一特征值下界估计
  • 2.2 关于定理0(Lichnerowicz)
  • 第二章 部分定理证明及解析
  • 3.1 关于定理1(1)及定理2的证明
  • 3.2 关于定理3的证明
  • 3.3 关于定理5和定理6的证明
  • 参考文献
  • 致谢
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    紧致Riemann流形第一特征值估计
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