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edition: [3 Sub ed.]
Authors: Frank Morgan
serie:
ISBN : 0125068514, 9780125068512
publisher: Academic Press Inc
publish year: 2003
pages: 226
language: English
ebook format : PDF (It will be converted to PDF, EPUB OR AZW3 if requested by the user)
file size: 8 Mb
Cover ......Page 1
Date-line ......Page 2
Contents ......Page 3
Preface ......Page 4
1. Geometric Measure Theory ......Page 7
2. Measures ......Page 13
3. Lipschitz Functions and Rectifiable Sets ......Page 27
4. Normal and Rectifiable Currents ......Page 41
5. The Compactness Theorem and the Existence of Area-Minimizing Surfaces ......Page 65
6. Examples of Area-Minimizing Surfaces ......Page 73
7. The Approximation Theorem ......Page 83
8. Survey of Regularity Results ......Page 87
9. Monotonicity and Oriented Tangent Cones ......Page 93
10. The Regularity of Area-Minimizing Hypersurfaces ......Page 103
11. Flat Chains Modulo $\\nu$, Varifolds, and $(M,\\varepsilon,\\delta$-Minimal Sets ......Page 111
12. Miscellaneous Useful Results ......Page 119
13. Soap Bubble Clusters ......Page 127
14. Proof of Double Bubble Conjecture ......Page 147
15. The Hexagonal Honeycomb and Kelvin Conjectures ......Page 163
16. Immiscible Fluids and Crystals ......Page 179
17. Isoperimetric Theorems in General Codimension ......Page 187
Solutions to Exercises ......Page 191
Bibliography ......Page 209
Index of Symbols ......Page 223
Name Index ......Page 227
Subject Index ......Page 229
