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.
Lecturer
Date
8th October ~ 30th December, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday,Wednesday | 15:20 - 16:55 | A6-101 | Zoom 17 | 442 374 5045 | BIMSA |
Prerequisite
Real analysis, Riemannian geometry.
Syllabus
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
Reference
[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。
Audience
Advanced Undergraduate
, Graduate
Video Public
No
Notes Public
Yes
Language
Chinese
Lecturer Intro
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.