An introduction to Plateau’s problem in arbitrary dimension
Student No.:50
Time:Mon/Wed 15:10-17:00, 2015-07-20 ~ 2015-08-12
Instructor:Xiangyu Liang  [University of Paris Sud 11]
Place:Conference Room 1, Floor 1, Jin Chun Yuan West Building
Starting Date:2015-7-20
Ending Date:2015-8-12




One of the main topics in geometric measure theory is Plateau’s problem, which aims at important progress in understanding the regularity and existence of physical objects that have certain minimizing property, such as soap films. Lots of notions of minimality have been introduced to modernize plateau’s problem, such as minimal surfaces, mass minimizing or size minimizing currents, stationary varifolds, and minimal sets, etc.

In this course, we will introduce necessary preliminaries: Hausdorff measure, Lipschitz maps, rectifiable sets, Federer-Fleming projection, etc. in the first part. In the second part of the course, we will discuss different mathematical approaches to Plateau’s problem.




Real analysis (a graduate level or advanced undergraduate level course is recommended).




H. Federer, Geometric measure theory.

P. Mattila, Geometry of Sets and Measures in Euclidean Spaces.

G. David & S. Semmes, Uniform Rectifiability and Quasiminimizing Sets of Arbitrary Codimension.

L. Simon, Lectures on geometric measure theory