Geometric Measure Theory
A Beginner's Guide
4th Edition
Published on 27. October 2008
Book
Hardback
264 pages
978-0-12-374444-9 (ISBN)
Description
Geometric Measure Theory, Fourth Edition, is an excellent text for introducing ideas from geometric measure theory and the calculus of variations to beginning graduate students and researchers.This updated edition contains abundant illustrations, examples, exercises, and solutions; and the latest results on soap bubble clusters, including a new chapter on Double Bubbles in Spheres, Gauss Space, and Tori. It also includes a new chapter on Manifolds with Density and Perelman's Proof of the Poincare Conjecture.This text is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Morgan emphasizes geometry over proofs and technicalities providing a fast and efficient insight into many aspects of the subject.
Reviews / Votes
"The text is simply unique. It doesn't compare to any other because its goals are different. It cannot be used as the only source of information for learning GMT, yet learning this subject without owning a copy of this book would be ridiculous since it gives a fast and efficient insight in many aspects of the theory.? --Thierry De Pauw, niversite catholique de Louvain, Belgium"The book is unique in its format and exposition. Without it, it would be difficult to get in touch with the subject. It paves the way to more advanced books. All other books on the market about this subject are rather technical and difficult to read for an inexperienced student.? --Stefan Wenger, Courant Institute of Math, New York UniversityMore details
Edition
4th edition
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
College/higher education
Advanced graduate students and researchers in mathematics.
Edition type
New edition
Dimensions
Height: 229 mm
Width: 152 mm
Weight
610 gr
ISBN-13
978-0-12-374444-9 (9780123744449)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Book
04/2016
5th Edition
Academic Press
€91.60
Shipment within 15-20 days
Additional editions
E-Book
09/2008
4th Edition
Academic Press
€47.99
Available for download
Previous edition
Book
08/2000
3rd Edition
Academic Press
€89.13
Article exhausted; check for reprint
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
Geometric Measure TheoryMeasuresLipschitz Functions and Rectifiable SetsNormal and Rectifiable CurrentsThe Compactness Theorem and the Existence of Area-Minimizing SurfacesExamples of Area-Minimizing SurfacesThe Approximation Theorem Survey of Regularity ResultsMonotonicity and Oriented Tangent ConesThe Regularity of Area-Minimizing HypersurfacesFlat Chains Modulo v, Varifolds, and (M,E,)-Minimal SetsMiscellaneous Useful ResultsSoap Bubble ClustersProof of Double Bubble ConjectureThe Hexagonal Honeycomb and Kelvin ConjecturesImmiscible Fluids and CrystalsIsoperimetric Theorems in General CodimensionManifolds with Density and Perelman's Proof of the Poincare ConjectureDouble Bubbles in Spheres, Gauss Space, and ToriSolutions to Exercises