Geometric Measure Theory: A Beginner's Guide 2nd Edition
Author(s): Frank Morgan (Author)
Publisher: Academic Press
Publication Date: 6 May 1995
Edition: 2nd
Language: English
Print length: 175 pages
ISBN-10: 0125068573
ISBN-13: 9780125068574
Book Description
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 and abundant illustrations and examples. This Second Edition features a new chapter on soap bubbles as well as updated sections addressing volume constraints, surfaces in manifolds, free boundaries, and Besicovitch constant results. The text will introduce newcomers to the field and appeal to mathematicians working in the field.
Editorial Reviews
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
From the Back Cover
Geometric measure theory is the mathematical framework for the study of crystal growth, the geometry of clusters of soap bubbles, and similar structures involving minimization of surface energy. Beautiful mathematics comes into play when a group of bubbles forms a cluster and physically solves the complicated mathematical problem of minimizing surface energy.
This Second Edition, intended for newcomers to the field of geometric measure theory, emphasizes geometry over proofs and technicalities, and includes a bibliography, abundant illustrations, exercises, and examples. Old hands will enjoy it as well, especially its new features: a new chapter on soap bubbles, as well as updated sections addressing volume contraints, surfaces in manifolds, free boundaries, general integrands, calibrations, and the recent disproof of Kelvin’s Conjecture. The text will introduce newcomers to the field and appeal to those working in the field.
Frank Morgan works in minimal surfaces and studies the behavior and structure of minimizers in various settings. He is also the author of Riemannian Geometry: A Beginners Guide and Calculus Life.
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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