Geometric Measure Theory

Geometric Measure Theory : 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 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.
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Product details

  • Hardback | 264 pages
  • 157.48 x 226.06 x 20.32mm | 521.63g
  • Academic Press Inc
  • San Diego, United States
  • English
  • 4th edition
  • 012374444X
  • 9780123744449
  • 1,253,591

Review quote

"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
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About 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.
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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 Poincare Conjecture
Double Bubbles in Spheres, Gauss Space, and Tori
Solutions to Exercises
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Review Text

"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 "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
show more

Rating details

5 ratings
4.2 out of 5 stars
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4 80% (4)
3 0% (0)
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