Geometric Measure Theory : A Beginner's Guide.
Title:
Geometric Measure Theory : A Beginner's Guide.
Author:
Morgan, Frank.
ISBN:
9780080525600
Personal Author:
Edition:
3rd ed.
Physical Description:
1 online resource (239 pages)
Contents:
Front Cover -- Geometric Measure Theory -- Copyright Page -- Contents -- Preface -- Chapter 1. Geometric Measure Theory -- Chapter 2. Measures -- Chapter 3. Lipschitz Functions and Rectifiable Sets -- Chapter 4. Normal and Rectifiable Currents -- Chapter 5. The Compactness Theorem and the Existence of Area-Minimizing Surfaces -- Chapter 6. Examples of Area-Minimizing Surfaces -- Chapter 7. The Approximation Theorem -- Chapter 8. Survey of Regularity Results -- Chapter 9. Monotonicity and Oriented Tangent Cones -- Chapter 10. The Regularity of Area-Minimizing Hypersurfaces -- Chapter 11. Flat Chains Modulo v, Varifolds, and (M, ε, δ)-Minimal Sets -- Chapter 12. Miscellaneous Useful Results -- Chapter 13. Soap Bubble Clusters -- Chapter 14. Proof of Double Bubble Conjecture -- Chapter 15. The Hexagonal Honeycomb and Kelvin Conjectures -- Chapter 16. Immiscible Fluids and Crystals -- Chapter 17. Isoperimetric Theorems in General Codimension -- Solutions to Exercises -- Bibliography -- Index of Symbols -- Name Index -- Subject Index -- Color Plate Section.
Abstract:
Geometric measure theory has become increasingly essential to geometry as well as numerous and varied physical applications. The third edition of this leading text/reference introduces the theory, the framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Over the past thirty years, this theory has contributed to major advances in geometry and analysis including, for example, the original proof of the positive mass conjecture in cosmology. This third edition of Geometric Measure Theory: A Beginner's Guide presents, for the first time in print, the proofs of the double bubble and the hexagonal honeycomb conjectures. Four new chapters lead the reader through treatments of the Weaire-Phelan counterexample of Kelvin's conjecture, Almgren's optimal isoperimetric inequality, and immiscible fluids and crystals. The abundant illustrations, examples, exercises, and solutions in this book will enhance its reputation as the most accessible introduction to the subject.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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