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
Gaoming Wang
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