An Introduction to Minimal Surfaces
I will cover most of the topics from Colding and Minicozzi's book. If time permits, I will introduce recent developments on stable Bernstein problems and μ-bubbles.
讲师
日期
2025年02月20日 至 05月22日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一,周四 | 09:50 - 11:25 | A3-1-101 | ZOOM 03 | 242 742 6089 | BIMSA |
修课要求
Riemannian geometry
课程大纲
1. Basic theory of minimal surfaces
2. Simons' equation and Schoen-Simon-Yau L^p curvature estimates
3. Weak convergence and Existence results
4. Min-Max constructions
5. Minimal surfaces in three-manifolds
2. Simons' equation and Schoen-Simon-Yau L^p curvature estimates
3. Weak convergence and Existence results
4. Min-Max constructions
5. Minimal surfaces in three-manifolds
参考资料
(1) Tobias Colding and William Minicozzi II, A Course in Minimal Surfaces
(2) Xin Zhou, Lecture Notes on Minimal Surfaces, Link: https://sites.google.com/cornell.edu/xinzhou
(3) Simon Brendle, The isoperimetric inequality for a minimal submanifold in Euclidean space
(4) Doris Fischer-Colbrie and Richard Schoen, The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
(2) Xin Zhou, Lecture Notes on Minimal Surfaces, Link: https://sites.google.com/cornell.edu/xinzhou
(3) Simon Brendle, The isoperimetric inequality for a minimal submanifold in Euclidean space
(4) Doris Fischer-Colbrie and Richard Schoen, The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
听众
Undergraduate
, Advanced Undergraduate
, Graduate
, 博士后
, Researcher
视频公开
公开
笔记公开
公开
语言
中文
, 英文
讲师介绍
我的研究方向是几何分析和广义相对论，目前主要研究标量曲率和广义相对论中的几何问题。我应用偏微分方程，特别是椭圆方程，来研究几何问题。