Herbert Federer rebuilt the subject from the ground up. His book is not merely a textbook; it is a complete, self-contained axiomatic foundation for analysis on rectifiable sets, currents (his generalization of distributions to surfaces), and varifolds. The is sought after specifically because the book is:
First published in 1969, this treatise systematically developed GMT to solve classical problems like the Plateau Problem federer geometric measure theory pdf
I can then recommend the specific chapters or supplementary notes that will be most helpful for your level! Herbert Federer rebuilt the subject from the ground up
If you want a of a modern geometric measure theory text that covers much of Federer’s material: If you want a of a modern geometric
Federer’s book is an introduction. It assumes:
Due to the difficulty of the original text, many students use "bridge" books before tackling Federer directly. If you find the PDF too dense, consider these resources:
: The final chapters apply these theories to the calculus of variations , detailing the Regularity Theorem for area-minimizing surfaces and establishing that singular sets have a specific optimal codimension. Accessing the Material Geometric Measure Theory: A Beginner's Guide