Online reference about Geometric Measure Theory.

Question

I would like to find an online reference about the basics of Geometric Measure Theory. The reference should treat such things as regions and isoperimetric surfaces. Can you tell me, where I can find something like this? Every help will be appreciated.

Answer 1

The textbook by Hebert Federer entitled Geometric Measure Theory is standard and reasonably comprehensive. You might also wish to look at Frank Morgan's Geometric Measure Theory: A Beginner's Guide which is shorter in length but also covers some important topics.

Answer 2

This book (Herbert Federer, Geometric Measure Theory, Classics in Mathematics) is my personal favorite for studying Geometric Measure Theory.

Also here you may have a good reference source for studying GMT.

Answer 3

Be advised that Federer's book is not for newcomers to the subject (and it's not an online reference anyway).

• An accessible introduction to isoperimetric and related inequalities is The Brunn-Minkowski inequality by Gardner. It focuses on the volume of subsets of $\mathbb R^n$, thus avoiding most of the GMT machinery.
• A somewhat dated, but still good, overview of GMT is in Colloquium lectures on geometric measure theory by Federer.
• EoM article goes through some key terms of the subject and has a good list of references. "Geometric measure theory. A beginner's guide" by Morgan is not a bad place to start.

Answer 4

I would like to propose two of my favorite geometric measure theory texts which are freely available online. The first one is "Sets of finite perimeter" by Maggi. The book is published by Cambridge University Press; but a draft is available online in Maggi

The other text (rather more advanced than Maggi) is the lectures by Leon Simon. This is a non-official second version of his classic book, Introduction to Geometric Measure Theory; and is available online at the author's webpage: Simon