Morgan Geometric Measure Theory

A Beginner's Guide
4. Auflage 2008
ISBN: 978-0-08-092240-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 264 Seiten, Web PDF

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.

Autoren/Hrsg.

Morgan, Frank

Inhaltsverzeichnis

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