Lectures on Geometric Measure Theory

Abstract

These notes grew out of lectures given by the author at the Institut für Angewandte Mathematik, Heidelberg University, and at the Centre for Mathematical Analysis, Australian National Unviersity

A central aim was to give the basic ideas of Geometric Measure Theory in a style readily accessible to analysts. I have tried to keep the notes as brief as possible, subject to the constraint of covering the really important and central ideas. There have of course been omissions; in an expanded version of these notes (which I hope to write in the near future), topics which would obviously have a high priority for inclusion are the theory of flat chains, further applications of G.M.T. to geometric variational problems, P.D.E. aspects of the theory, and boundary regularity theory.