Minimal Hypersurfaces: Stability, Regularity, and its application
This course focuses on the theory of minimal surfaces, with particular emphasis on stable minimal hypersurfaces. There have been significant developments in the study of stability and its geometric consequences. We will introduce the fundamental results on stable minimal hypersurfaces, including curvature estimates, the Bernstein theorem, regularity theory, and compactness results. Applications to scalar curvature problems and general relativity will also be discussed.
讲师
日期
2026年03月05日 至 06月25日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周四 | 14:20 - 16:55 | A3-1-103 | ZOOM 04 | 482 240 1589 | BIMSA |
修课要求
Riemannian geometry, Partial differential equations
课程大纲
1. First and second variation formulas, the Bernstein problem, and curvature estimates for stable minimal hypersurfaces.
2. Regularity theorems and compactness results, including the work of Schoen–Simon, Wickramasekera, and Bellettini.
3. The dimension reduction techniques due to Schoen-Yau, and their applications to geometric and physical problems.
2. Regularity theorems and compactness results, including the work of Schoen–Simon, Wickramasekera, and Bellettini.
3. The dimension reduction techniques due to Schoen-Yau, and their applications to geometric and physical problems.
听众
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
王高明从香港中文大学毕业，其导师为李文俊 (Martin Li) 教授。他曾经在康奈尔大学访问一年，而后在YMSC做博士后。目前他主要研究兴趣为黎曼几何，几何分析，以及几何偏微分方程。