|An introduction to the theory of minimal sets|
|Time：||Tue/Thu 15:10-17:00, 2014-07-08 ~ 2014-08-14|
|Instructor：||Xiangyu Liang [University of Paris Sud 11]|
|Place：||Conference Room 3, Floor 2, Jin Chun Yuan West Building|
The theory of minimal sets was introduced by F.J. Almgren to modernize Plateau’s problem, which aims at understanding physical objects that admit certain minimizing property, such as Soap films. The study of existence and regularity for minimal sets is one of the central interest in Geometric measure theory.
We will try to make this course self-containing. In the first half, we will introduce basic concepts and knowledges (especially those about Lipschitz maps and rectifiable sets) that are necessary for the study of minimal sets : Covering theorem, Hausdorff measure, Lipschitz maps, Lipschitz extension, area and coarea formula for rectifiable sets, Federer-Fleming projection, etc. Then we will discuss minimal setsin the second half.
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.