Preface
1 Geometric Measure Theory
2 Measures
3 Lipschitz Functions and Rectifiable Sets
4 Normal and Rectifiable Currents
5 The Compactness Theorem and the Existence of Area-Minimizing Surfaces
6 Examples of Area-Minimizing Surfaces
7 The Approximation Theorem
8 Survey of Regularity Results
9 Monotonicity and Oriented Tangent Cones
10 The Regularity of Area-Minimizing Hypersurfaces
11 Flat Chains Modulo v Varifolds, and-Minimal Sets
12 Miscellaneous Useful Results
13 Soap Bubble Clusters
14 Proof of Double Bubble Conjecture
15 The Hexagonal Honeycomb and Kelvin Conjectures
16 Immiscible Fluids and Crystals
17 Isoperimetric Theorems in General Codimension
18 Manifolds with Density and Perelman's Proof of the Poincare Conjecture
19 Double Bubbles in Spheres, Gauss Space, and Tori
Solutions to Exercises
Bibliography
Index of Symbols
Name Index
Subject Index
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