Geometric Measure Theory - Regularity
unofficial course @ Princeton
Description
This is the page for an unofficial course at Princeton taught by the lovely Prof. Paul Minter that I had the pleasure of attending during Spring 2023. Below is the course description and some resources about the topic.
“The aim of this course is to cover several key results within geometric measure theory, in particular the regularity theory of minimal surfaces. One key idea is that of excess decay, arising from a suitable blow-up (i.e. linearisation) procedure. Topics covered are: tangent cones and single set stratification, Schoen-Simon regularity theory for stable minimal hypersurfaces (with small singular sets), Allard regularity for stationary varifolds, Simon’s cylindrical tangent cones, and Wickramasekera’s regularity theory for stable minimal hypersurfaces.”
I have no idea how I managed to follow along, but I did and I am very proud. This class gave me some very cool ideas for DL theory, email me if interested :)
Reading List
- As always, Leon Simon’s textbook (builds toward varifolds and integration).
- Belletini’s extension of Schoen-Simon regularity theory via De-Giorgi iteration.
- Allard’s original regularity paper.
- Leon Simon’s cylindrical cones paper.
- Wickramasekera’s amazing paper on stable minimal hypersurfaces.