Geometric measure theory. A beginner's guide

✍ Scribed by Morgan, Frank

• Publisher: Academic Press is an imprint of Elsevier
• Year: 2016
• Tongue: English
• Leaves: 260
• Edition: Fifth edition
• Category: Library

✦ Table of Contents

Title page......Page 1
Dedication......Page 3
ISBN: 978-0-12-804489-6......Page 4
Preface......Page 5
Table of contents......Page 7
1 Geometric Measure Theory......Page 9
2 Measures......Page 16
3 Lipschitz Functions and Rectifiable Sets......Page 29
4 Normal and Rectifiable Currents......Page 43
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 82
8 Survey of Regularity Results......Page 85
9 Monotonicity and Oriented Tangent Cones......Page 90
10 The Regularity of Area-Minimizing Hypersurfaces......Page 98
11 Flat Chains Modulo ν, Varifolds, and (M, ε, δ)-Minimal Sets......Page 106
12 Miscellaneous Useful Results......Page 112
13 Soap Bubble Clusters......Page 120
14 Proof of Double Bubble Conjecture......Page 141
15 The Hexagonal Honeycomb and Kelvin Conjectures......Page 157
16 Immiscible Fluidsand Crystals......Page 171
17 Isoperimetric Theoremsin General Codimension......Page 177
18 Manifolds with Density and Perelman’s Proof of the Poincaré Conjecture......Page 181
19 Double Bubbles in Spheres, Gauss Space, and Tori......Page 194
20 The Log-Convex Density Theorem......Page 202
Solutions to Exercises......Page 209
Bibliography......Page 231
Index of Symbols......Page 251
Name Index......Page 253
Subject Index......Page 255
On my way......Page 260

✦ Subjects

Geometric measure theory