Geometric Measure Theory
A Beginner's Guide
2nd Edition
Published on 2. May 1995
Book
Hardback
175 pages
978-0-12-506857-4 (ISBN)
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.
Reviews / Votes
"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
More details
Edition
2nd edition
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
College/higher education
Dimensions
Height: 229 mm
Width: 151 mm
Weight
440 gr
ISBN-13
978-0-12-506857-4 (9780125068574)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Book
08/2000
3rd Edition
Academic Press
€89.13
Article exhausted; check for reprint
Additional editions
E-Book
05/2014
2nd Edition
Academic Press
€54.95
Available for download
Person
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.
Content
Preface. Geometric Measure Theory. Measures. Lipschitz Functions and Rectifiable Sets. Normal and Rectifiable Currents. The Compactness Theorem and the Existence of Area-Minimizing Surfaces. Examples of Area-Minimizing Surfaces. The Approximation Theorem. Survey of Regularity Results. Monotonicity and Oriented Tangent Cones. The Regularity of Area-Minimizing Hypersurfaces. Flat Chains Modulo (, Varifolds, and (M, (, ()-Minimal Sets. Miscellaneous Useful Results. Soap Bubble Clusters. Solutions to Exercises. Bibliography. Index of Symbols. Author Index. Subject Index.