Geometric Measure Theory

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Geometric Measure Theory,

Edition 4 A Beginner's Guide

Editors: By Frank Morgan

Publication Date: 09 Sep 2008

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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.

About the author

By Frank Morgan, Dennis Meenan '54 Third Century Professor of Mathematics at Williams College.

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 Poincaré ConjectureDouble Bubbles in Spheres, Gauss Space, and ToriSolutions to Exercises

ISBN: 9780123744449

Page Count: 264

Retail Price (USD) :

9780120887354; 9780123694270; 0121160513

Advanced graduate students and researchers in mathematics

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