Geometric Measure Theory: A Beginner's Guide

Rating:
Summary: Up-to-date reference.
Review: This thin book (175 pages) provides the newcomer or graduate student with an illustrated introduction to geometric measure theory: the basic ideas, terminology, and results. The author has included a few fundamental arguments and a superficial discussion of the regularity theory, but his goal is merely to introduce the subject and make the standard text, "Geometric Measure Theory" by Federer, more accesible. This second edition includes updated material and references, corrections, and a new chapter on soap bubble clusters.

Its contents are: Measures, Lipschitz functions and rectifiable sets, normal and rectifiable currents, the completeness theorem, area-minimizing surfaces, the approximation theorem, regualrity results, monotonicity and oriented tanget cones, flat chains, varifolds, minimal sets, soap bubble clusters.

Includes excercises, plenty of illustrations, and extensive references.

Highly useful for advanced undergraduate and graduate students in analysis and geometry. The "next step" for fractal geometers.

If you want to buy it maybe it should be better to wait for the third edition to appear by June 2000.

Please check my other reviews (just click on my name above).