Introduction to Geometric Measure Theory
Geometric Measure Theory is concerned with the rigorous analysis of sets and functions that arise in geometry and analysis, particularly those exhibiting irregular or fractal behavior. It provides a framework for extending classical notions of length, area, and volume to highly non-smooth contexts. This course introduces the foundational concepts of Hausdorff measure, rectifiability, and currents, emphasizing the application to minimal surfaces.
Lecturer
Date
10th September, 2025 ~ 7th January, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 19:20 - 21:45 | A3-2-301 | ZOOM 03 | 242 742 6089 | BIMSA |
Prerequisite
Real analysis, Riemannian geometry
Syllabus
1. Hausdorff measure
2. Lipschitz functions
3. Rectifiable sets
4. Varifolds
5. The Allard Regularity Theorem
6. Currents
7. Area Minimizing Currents
2. Lipschitz functions
3. Rectifiable sets
4. Varifolds
5. The Allard Regularity Theorem
6. Currents
7. Area Minimizing Currents
Reference
1. Introduction to Geometric Measure Theory, Leon Simon
2. Geometric Measure Theory, Herbert Federer
3. Geometric Measure Theory----An Introduction, Fanghua Lin and Xiaoping Yang
2. Geometric Measure Theory, Herbert Federer
3. Geometric Measure Theory----An Introduction, Fanghua Lin and Xiaoping Yang
Audience
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.