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Preface | p. vii |
Geometric Measure Theory | p. 1 |
Measures | p. 7 |
Lipschitz Functions and Rectifiable Sets | p. 21 |
Normal and Rectifiable Currents | p. 35 |
The Compactness Theorem and the Existence of Area-Minimizing Surfaces | p. 59 |
Examples of Area-Minimizing Surfaces | p. 67 |
The Approximation Theorem | p. 77 |
Survey of Regularity Results | p. 81 |
Monotonicity and Oriented Tangent Cones | p. 87 |
The Regularity of Area-Minimizing Hypersurfaces | p. 97 |
Flat Chains Modulo [upsilon], Varifolds, and (M, [varepsilon], [delta])-Minimal Sets | p. 105 |
Miscellaneous Useful Results | p. 113 |
Soap Bubble Clusters | p. 121 |
Proof of Double Bubble Conjecture | p. 141 |
The Hexagonal Honeycomb and Kelvin Conjectures | p. 157 |
Immiscible Fluids and Crystals | p. 173 |
Isoperimetric Theorems in General Codimension | p. 181 |
Solutions to Exercises | p. 185 |
Bibliography | p. 203 |
Index of Symbols | p. 217 |
Name Index | p. 221 |
Subject Index | p. 223 |
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