Geometric Measure Theory
4th Edition
A Beginner's Guide
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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 Poincaré 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.
Key Features
New to the 4th edition:
- Abundant illustrations, examples, exercises, and solutions.
- The latest results on soap bubble clusters, including a new chapter on "Double Bubbles in Spheres, Gauss Space, and Tori."
- A new chapter on "Manifolds with Density and Perelman's Proof of the Poincaré Conjecture."
- Contributions by undergraduates.
Readership
Advanced graduate students and researchers in mathematics.
Table of Contents
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 v, Varifolds, and (M,E,)-Minimal Sets Miscellaneous Useful Results Soap Bubble Clusters Proof of Double Bubble Conjecture The Hexagonal Honeycomb and Kelvin Conjectures Immiscible Fluids and Crystals Isoperimetric Theorems in General Codimension Manifolds with Density and Perelman's Proof of the Poincaré Conjecture Double Bubbles in Spheres, Gauss Space, and Tori Solutions to Exercises
Details
- No. of pages:
- 264
- Language:
- English
- Copyright:
- © Academic Press 2009
- Published:
- 9th September 2008
- Imprint:
- Academic Press
- eBook ISBN:
- 9780080922409
About the Author
Frank Morgan
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.
Affiliations and Expertise
Williams College, Williamstown, MA, USA
Reviews
“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 University