Selected topics in geometric analysis Ⅱ
This course is divided into three main parts. The first part presents some basic tools that are necessary for research in geometric analysis. The second part is on harmonic functions and eigenvalue problems. The last part gives an outline of the theory of the heat equation on a Riemannian manifold.
讲师
日期
2024年10月08日 至 12月30日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一,周三 | 15:20 - 16:55 | A6-101 | Zoom 17 | 442 374 5045 | BIMSA |
修课要求
Real analysis, Riemannian geometry.
课程大纲
1. Variational formulas
2. Comparison theorems and Cheeger-Gromoll splitting theorem
3. Poincare inequality and Sobolev inequality
4. Harmonic functions
5. Eigenvalue problems
6. The heat equation
7. Gradient estimate and Harnack inequality
8. Regularity theory
2. Comparison theorems and Cheeger-Gromoll splitting theorem
3. Poincare inequality and Sobolev inequality
4. Harmonic functions
5. Eigenvalue problems
6. The heat equation
7. Gradient estimate and Harnack inequality
8. Regularity theory
参考资料
[1] Peter Li, Geometric Analysis, Cambridge Studies in Advanced Mathematics, Vol. 134, Cambridge University Press, Cambridge, 2012.
[2] 丘成桐，孙理察，微分几何讲义，高等教育出版社，北京，2004。
[2] 丘成桐，孙理察，微分几何讲义，高等教育出版社，北京，2004。
听众
Advanced Undergraduate
, Graduate
视频公开
不公开
笔记公开
公开
语言
中文
讲师介绍
Liangdi Zhang received his Ph.D. degree from Zhejiang University in June 2021. He worked as a postdoc at Beijing Institute of Mathematical Sciences and Applications (BIMSA) and Tsinghua University from August 2021 to August 2023. He is currently an assistant professor at BIMSA. His research interests include differential geometry and geometric analysis.