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Sichuan University

几何中的一类非线性四阶PDE

Sichuan University via XuetangX

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本课程以几何为出发点来介绍一类线性化的 Monge-Ampere 方程，即仿射
几何中的极大曲面方程和环簇几何中的数量曲率方程。通过课程，希望研
究生能快速进入几何的相关问题研究。



Syllabus

  • 绪论
    • 绪论
  • 第一章 仿射几何基础
    • 1.1 仿射微分几何基础
  • 第二章 环簇几何基础
    • 2.1 环簇上的极值度量
  • 第三章 线性化Monge-Ampere方程理论
    • 3.1 Abreu方程
    • 3.2 线性化 Monge-Ampère 方程
  • 第四章 Bernstein性质
    • 4.1 Bernstein 性质
    • 4.2 仿射极大超曲面的 Bernstein 问题
    • 4.3 关于Calabi度量的仿射 Bernstein 问题
  • 期末考试

    Taught by

    Li An-Min, Li Sheng, Baihui Chen, Zejun Hu, and Ruiwei Xu

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