Geometric Measure Theory: A Beginner's Guide

by Frank Morgan

Overview

Geometric Measure Theory: A Beginner's Guide, Fifth Edition provides the framework readers need to understand the structure of a crystal, a soap bubble cluster, or a universe.

The book is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Brevity, clarity, and scope make this classic book an excellent introduction to more complex ideas from geometric measure theory and the calculus of variations for beginning graduate students and researchers.

Morgan emphasizes geometry over proofs and technicalities, providing a fast and efficient insight into many aspects of the subject, with new coverage to this edition including topical coverage of the Log Convex Density Conjecture, a major new theorem at the center of an area of mathematics that has exploded since its appearance in Perelman's proof of the Poincaré conjecture, and new topical coverage of manifolds taking into account all recent research advances in theory and applications.

Product Details

ISBN-13:	9780080525600
Publisher:	Elsevier Science & Technology Books
Publication date:	08/22/2000
Sold by:	Barnes & Noble
Format:	eBook
Pages:	227
File size:	10 MB

About the Author

Frank Morgan is the Dennis Meenan '54 Third Century Professor of Mathematics at Williams College. He obtained his B.S. from MIT and his M.S. and Ph.D. from Princeton University. His research interest lies in minimal surfaces, studying the behavior and structure of minimizers in various settings. He has also written Riemannian Geometry: A Beginner's Guide, Calculus Lite, and most recently The Math Chat Book, based on his television program and column on the Mathematical Association of America Web site.

Table of Contents

Geometric Measure TheoryMeasuresLipschitz Functions and Rectifiable SetsNormal and Rectifiable CurrentsThe Compactness Theorem and the Existence of Area-Minimizing SurfacesExamples of Area-Minimizing SurfacesThe Approximation Theorem Survey of Regularity ResultsMonotonicity and Oriented Tangent ConesThe Regularity of Area-Minimizing HypersurfacesFlat Chains Modulo v, Varifolds, and (M,E,)-Minimal SetsMiscellaneous Useful ResultsSoap Bubble ClustersProof of Double Bubble ConjectureThe Hexagonal Honeycomb and Kelvin ConjecturesImmiscible Fluids and CrystalsIsoperimetric Theorems in General CodimensionManifolds with Density and Perelman's Proof of the Poincaré ConjectureDouble Bubbles in Spheres, Gauss Space, and ToriSolutions to Exercises

What People are Saying About This

From the Publisher

Brevity, clarity and scope make this classic text excellent for introducing ideas from geometric measure theory and the calculus of variations to beginning graduate students and researchers

Editorial Reviews

This graduate textbook introduces the basic ideas, terminology, and results of geometric measure theory for students who have taken a course in real analysis. The third edition adds four chapters that present proofs of the Double Bubble and Hexagonal Honeycomb conjectures and recent results in immiscible fluids and isoperimetric inequalities. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"Morgan’s book offers the best access I know into this difficult subject. It won’t make the reader an expert, but it does open the door to more detailed treatments. An excellent bibliography is provided." —MAA Reviews

From the Publisher