BIMSA > Introduction to Geometric Measure Theory
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.
Professor Lars Aake Andersson
讲师
张一岳
日期
2025年09月10日 至 2026年01月07日
位置
Weekday Time Venue Online ID Password
周三 19:20 - 21:45 A3-2-301 ZOOM 03 242 742 6089 BIMSA
修课要求
Real analysis, Riemannian geometry
课程大纲
1. Hausdorff measure
2. Lipschitz functions
3. Rectifiable sets
4. Varifolds
5. The Allard Regularity Theorem
6. Currents
7. Area Minimizing Currents
参考资料
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
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
讲师介绍
我的研究方向是几何分析和广义相对论，目前主要研究标量曲率和广义相对论中的几何问题。我应用偏微分方程，特别是椭圆方程，来研究几何问题。