Geometric Measure Theory
by Morgan, Frank; Bredt, James F.Edition: 2nd
Format: Hardcover
Pub. Date: 1995-04-01
Publisher(s): Academic Pr
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Summary
Geometric measure theory is the mathematical framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Morgan emphasizes geometry over proofs and technicalities, and includes a bibliography and abundant illustrations and examples. This Second Edition features a new chapter on soap bubbles as well as updated sections addressing volume constraints, surfaces in manifolds, free boundaries, and Besicovitch constant results. The text will introduce newcomers to the field and appeal to mathematicians working in the field.
Table of Contents
| 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 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
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