Geometric Measure Theory: A Beginners Guide

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9780125068550: Geometric Measure Theory: A Beginners Guide

Geometric measure theory is the mathematical framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Morgan emphasizes geometry over proofs and technicalities, and includes a bibliography. This Second Edition features a new chapter on soap bubbles.

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From the Back Cover:

Geometric measure theory provides the framework to understand the structure of a crystal, a soap bubble cluster, or a universe. Over the past forty years it has contributed to major advances in geometry and analysis, including, for example, the original proof of the positive mass conjecture in cosmology. Undergraduates have made important contributions to the subject.
This third edition of Geometric Measure Theory: A Beginner's Guide presents, for the first time in print, the proofs of the Double Bubble Conjecture (equal and unequal volumes) and the Hexagonal Honeycomb Conjecture. Within four new chapters, readers are also led through treatments of the Weaire-Phelan counterexample to the Kelvin conjecture, Almgren's optimal isoperimetric inequality, 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.

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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Morgan, Frank
Published by Academic Pr (1988)
ISBN 10: 0125068557 ISBN 13: 9780125068550
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