Introduction to Geometric Measure Theory - Spring 2017 | ||
Lecturer | Prof. S. Wenger | |
Time
Start date |
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. Literature: |