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.
Lecturer
Date
5th March ~ 25th June, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Thursday | 14:20 - 16:55 | A3-1-103 | ZOOM 04 | 482 240 1589 | BIMSA |
Prerequisite
Riemannian geometry, Partial differential equations
Syllabus
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.
Audience
Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
Chinese
, English
Lecturer Intro
Gaoming Wang graduated from The Chinese University of Hong Kong under the supervison of Prof. Martin Man-Chun Li. He visited Cornell University for one year and was a PostDoc at the Yau Mathematical Sciences Center at Tsinghua University. His research interests primarily focus on Riemannian geometry, geometric analysis, and geometric partial differential equations.