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
5. Minimal surfaces in three-manifolds
2. Simons' equation and Schoen-Simon-Yau L^p curvature estimates
3. Weak convergence and Existence results
4. Min-Max constructions
5. Minimal surfaces in three-manifolds
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
(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
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.