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 (Colding-De Lellis's survey)
5. Minimal surfaces in three-manifolds
6. μ-bubbles (Chodosh-Li's paper)
2. Simons' equation and Schoen-Simon-Yau L^p curvature estimates
3. Weak convergence and Existence results
4. Min-Max constructions (Colding-De Lellis's survey)
5. Minimal surfaces in three-manifolds
6. μ-bubbles (Chodosh-Li's paper)
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
(5) Tobias H. Colding and Camillo De Lellis, The min-max construction of minimal surfaces
(6) Richard Schoen and Shing Tung Yau, On the proof of the positive mass conjecture in general relativity
(7) Otis Chodosh and Chao Li, Generalized soap bubbles and the topology of manifolds with positive 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
(5) Tobias H. Colding and Camillo De Lellis, The min-max construction of minimal surfaces
(6) Richard Schoen and Shing Tung Yau, On the proof of the positive mass conjecture in general relativity
(7) Otis Chodosh and Chao Li, Generalized soap bubbles and the topology of manifolds with positive 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。