|Introduction to Geometric Measure Theory - Spring 2019|
|Lecturer||Prof. S. Wenger|
Mondays 13:15 - 15:00 in Science de la terre 1.309 and Fridays 10:15-12:00 in Physics 2.52|
18 February 2019
The following problem, called Plateau's problem, lies at the origins of Geometric Measure Theory: Does every Jordan curve bound a surface of minimal area? The name goes back to the Belgian physicist Joseph Plateau who made extensive experiments with soap films in order to find an answer to this problem.
One of the principal achievements of Geometric Measure Theory has been to develop a sufficiently rich and powerful theory of surfaces which can be used to solve this problem and many related geometric variational problems.
This course provides an introduction to Geometric Measure Theory. Prerequisites are the course Mesure et Intégration (MA.3400/4400) and a good understanding of submanifolds and differential forms. A course on Functional Analysis is recommended but not strictly required.
Outline of course (might change slightly as we go along):
A) Review of measure theory:
Preliminary notes for the course.