|Introduction to Geometric Measure Theory - Spring 2017|
|Lecturer||Prof. S. Wenger|
Mondays 13:15 - 15:00 and Fridays 10:15-12:00, Science de la terre 2.301|
20 February 2017
Geometric Measure Theory (GMT) studies geometric properties of singular surfaces (of any dimension) through the use of measure theory. The following problem lies at the origins of GMT. Does every k-dimensional surface without boundary in Euclidean n-space bound a (k+1)-dimensional surface of minimal volume? One of the principal achievements of GMT has been to develop a sufficiently rich and powerful theory of surfaces in Euclidean space which can be used to solve this problem and many related geoemtric variational problems. GMT is a very active area of current research and has found applications in many areas of mathematics, far beyond the problem of area minimization.
In this course, we give a gentle introduction to Geometric Measure Theory. The only prerequisites are the courses Analysis 1 - 4. A course in (abstract) measure theory is useful but not required.
Outline of course (might change slightly as we go along):
A) Review of measure theory:
Preliminary notes for the course, taken by C. Guo and to be updated regularly during the semester.