Geometric Measure Theory
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Geometric Measure Theory : A Beginner's Guide

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Description

Geometric Measure Theory: A Beginner's Guide, Fifth Edition provides the framework readers need to understand the structure of a crystal, a soap bubble cluster, or a universe.

The book is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Brevity, clarity, and scope make this classic book an excellent introduction to more complex ideas from geometric measure theory and the calculus of variations for beginning graduate students and researchers.

Morgan emphasizes geometry over proofs and technicalities, providing a fast and efficient insight into many aspects of the subject, with new coverage to this edition including topical coverage of the Log Convex Density Conjecture, a major new theorem at the center of an area of mathematics that has exploded since its appearance in Perelman's proof of the Poincare conjecture, and new topical coverage of manifolds taking into account all recent research advances in theory and applications.
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Product details

  • Hardback | 272 pages
  • 152 x 229 x 19.05mm | 610g
  • Academic Press Inc
  • San Diego, United States
  • English
  • 5th edition
  • 0128044896
  • 9780128044896
  • 2,116,489

Review quote

"Morgan's book offers the best access I know into this difficult subject. It won't make the reader an expert, but it does open the door to more detailed treatments. An excellent bibliography is provided." --MAA Reviews, Geometric Measure Theory, Fifth Edition
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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
The Log-Convex Density Conjecture
Solutions to Exercises
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Review Text

"Morgan's book offers the best access I know into this difficult subject. It won't make the reader an expert, but it does open the door to more detailed treatments. An excellent bibliography is provided." -- MAA Reviews, Geometric Measure Theory, Fifth Edition
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Rating details

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