An Introduction to Geometric Measure Theory and Rectifiable Sets

Speaker: Vegard Hansen, Master student @ the University of Bergen

Abstract: Geometric measure theory is roughly speaking the study of geometric objects using the techniques of measure theory. Among the core concepts of this theory is the notion of rectifiable subsets. They provide a generalisation of manifolds to a class with a much less rigid structure. I will present the main ingredients in GMT, namely the Hausdorff measures and Lipschitz maps. Using these we will define the rectifiable sets, and discuss some of their properties.