Geometric Measure Theory: A Beginner's Guide

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9780125068512: Geometric Measure Theory: A Beginner's Guide

Geometric measure theory has become increasingly essential to geometry as well as numerous and varied physical applications. The third edition of this leading text/reference introduces the theory, the framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy.

Over the past thirty years, this theory has contributed to major advances in geometry and analysis including, for example, the original proof of the positive mass conjecture in cosmology.

This third edition of Geometric Measure Theory: A Beginner's Guide presents, for the first time in print, the proofs of the double bubble and the hexagonal honeycomb conjectures. Four new chapters lead the reader through treatments of the Weaire-Phelan counterexample of Kelvin's conjecture, Almgren's optimal isoperimetric inequality, and immiscible fluids and crystals. The abundant illustrations, examples, exercises, and solutions in this book will enhance its reputation as the most accessible introduction to the subject.

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Review:

"This second edition continues to present an accessible and up-to-date source of the major advances in geometric measure theory. The book is intended to give the uninitiated a meaningful introduction to the subject by presenting basic ideas, terminology, and results in a framework that minimizes the plethora of associated technicalities and details. The author accomplishes this objective with resounding success. Moreover, the book also serves as a useful reference for those claiming some degree of expertise in this area since it provides an easily digested, macroscopic view of the subject as a result of its evolution during the past thirty-five years."--MATH REVIEWS

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.

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