Overview
Geometric measure theory provides the framework to understand the structure of a crystal, a soap bubble cluster, or a universe. Measure Theory: A Beginner's Guide 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.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.
Synopsis
Geometric measure theory provides the framework to understand the structure of a crystal, a soap bubble cluster, or a universe. Measure Theory: A Beginner's Guide 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.
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.
Booknews
This graduate textbook introduces the basic ideas, terminology, and results of geometric measure theory for students who have taken a course in real analysis. The third edition adds four chapters that present proofs of the Double Bubble and Hexagonal Honeycomb conjectures and recent results in immiscible fluids and isoperimetric inequalities. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Editorials
From the Publisher
“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