Geometric Measure Theory
Academic Press Inc (Verlag)
978-0-12-374444-9 (ISBN)
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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.
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.
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
| Erscheint lt. Verlag | 27.10.2008 |
|---|---|
| Verlagsort | San Diego |
| Sprache | englisch |
| Maße | 152 x 229 mm |
| Gewicht | 610 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-12-374444-X / 012374444X |
| ISBN-13 | 978-0-12-374444-9 / 9780123744449 |
| Zustand | Neuware |
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