Introduction to Geometric Measure Theory, Fall 2021

Lectures: MWF 9:25am - 10:15, Pasquerilla Center 109

Office hours: TBD

Syllabus: GMT studies the geometry and analysis of sets by treating them as measures, and provides a powerful framework to study geometric variational problems, such as minimal surfaces and isoperimetic domains. In this course we will try to cover: Hausdorff measure, rectifiability, area/coarea formulae, BV functions, sets of finite perimeter, varifolds, first/second variation for area, regularity theorems for minimal surfaces due to Allard/DeGiorgi, currents, area-minimizing currents, Plateau's problem, optimal regularity for area-minimizing hypersurfaces.

Book: Simon, ``Introduction to geometric measure theory,'' available freely at https://web.stanford.edu/class/math285/. Other good references which we may partly follow are: Maggi, ``Sets of finite perimeter and geometric variational problems.'' Evans and Gariepy, ``Measure theory and find properties of functions.'' Federer's ``Geometric measure theory'' is a beautiful reference bible, but not super approachable.

Grade: TBD.

Problem sets: TBD.