Geometric Measure Theory, Third Edition: A Beginner's Guide

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9780125068512: Geometric Measure Theory, Third Edition: 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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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 Press (2000)
ISBN 10: 0125068514 ISBN 13: 9780125068512
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Frank Morgan
Published by Academic Press (2000)
ISBN 10: 0125068514 ISBN 13: 9780125068512
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