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.
Lecturer
Date
20th February ~ 22nd May, 2025
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday,Thursday | 09:50 - 11:25 | A3-1-101 | ZOOM 03 | 242 742 6089 | BIMSA |
Prerequisite
Riemannian geometry
Syllabus
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)
Reference
(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
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
Yes
Notes Public
Yes
Language
Chinese
, English
Lecturer Intro
I am interested in geometric analysis and general relativity. More specifically, I am working on problems related to scalar curvature and geometric problems from physics. I enjoy applying the tools from PDEs, especially elliptic PDEs, to study geometry.