Geometric Measure Theory (eBook)

A Beginner's Guide

Frank Morgan (Autor)

eBook Download: PDF

2008 | 4. Auflage
264 Seiten
Elsevier Science (Verlag)
978-0-08-092240-9 (ISBN)

Infos

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 Poincar? 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.

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 Poincar? Conjecture.'
* Contributions by undergraduates.

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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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.New to the 4th edition:* Abundant illustrations, examples, exercises, and solutions.* The latest results on soap bubble clusters, including a new chapter on "e;Double Bubbles in Spheres, Gauss Space, and Tori."e;* A new chapter on "e;Manifolds with Density and Perelman's Proof of the Poincare Conjecture."e;* Contributions by undergraduates.

Inhalt

Front Cover 1
Geometric Measure Theory A Beginner’s Guide 4
Copyright Page 5
Table Contents 6
Preface 8
Chapter 1. Geometric Measure Theory 10
Chapter 2. Measures 18
Chapter 3. Lipschitz Functions and Rectifiable Sets 32
Chapter 4. Normal and Rectifiable Currents 46
Chapter 5. The Compactness Theorem and the Existence of Area-Minimizing Surfaces 68
Chapter 6. Examples of Area-Minimizing Surfaces 76
Chapter 7. The Approximation Theorem 86
Chapter 8. Survey of Regularity Results 90
Chapter 9. Monotonicity and Oriented Tangent Cones 96
Chapter 10. The Regularity of Area-Minimizing Hypersurfaces 104
Chapter 11. Flat Chains Modulo ., Varifolds, and (M, e, d)-Minimal Sets 112
Chapter 12. Miscellaneous Useful Results 118
Chapter 13. Soap Bubble Clusters 126
Chapter 14. Proof of Double Bubble Conjecture 148
Chapter 15. The Hexagonal Honeycomb and Kelvin Conjectures 164
Chapter 16. Immiscible Fluids and Crystals 178
Chapter 17. Isoperimetric Theorems in General Codimension 184
Chapter 18. Manifolds with Density and Perelman’s Proof of the Poincaré Conjecture 188
Chapter 19. Double Bubbles in Spheres, Gauss Space, and Tori 202
Solutions to Exercises 210
Bibliography 232
Index of Symbols 250
Name Index 252
Subject Index 254

Produkt-Details

• Erscheint lt. Verlag: 9.9.2008
• Sprache: englisch
• Themenwelt: Schulbuch / Wörterbuch
• Themenwelt: Informatik ► Grafik / Design ► Film- / Video-Bearbeitung
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• ISBN-10: 0-08-092240-6 / 0080922406
• ISBN-13: 978-0-08-092240-9 / 9780080922409