Geometric Measure Theory. A Beginner's Guide

✍ Scribed by Frank Morgan (Auth.)

• Publisher: Elsevier Inc, Academic Press
• Year: 1988
• Tongue: English
• Leaves: 140
• Category: Library

✦ Synopsis

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. This Second Edition features a new chapter on soap bubbles

✦ Table of Contents

Content:
Dedication, Page ii
Front Matter, Page iii
Copyright, Page iv
Preface, Pages vii-viii
CHAPTER 1 - Geometric Measure Theory, Pages 1-6
CHAPTER 2 - Measures, Pages 7-20
CHAPTER 3 - Lipschitz Functions and Rectifiable Sets, Pages 21-35
CHAPTER 4 - Normal and Rectifiable Currents, Pages 37-58
CHAPTER 5 - The Compactness Theorem and the Existence of Area-Minimizing Surfaces, Pages 59-66
CHAPTER 6 - Examples of Area-Minimizing Surfaces, Pages 67-75
CHAPTER 7 - The Approximation Theorem, Pages 77-79
CHAPTER 8 - Survey of Regularity Results, Pages 81-85
CHAPTER 9 - Monotonicity and Oriented Tangent Cones, Pages 87-95
CHAPTER 10 - The Regularity of Area-Minimizing Hypersurfaces, Pages 97-105
CHAPTER 11 - Flat Chains Modulo v, Varifolds, and (M, ɛ, δ)-Minimal Sets, Pages 107-111
CHAPTER 12 - Miscellaneous Useful Results, Pages 113-117
Solutions to Exercises, Pages 119-134
Bibliography, Pages 135-137
Index of Symbols, Pages 139-140
Name Index, Page 141
Subject Index, Pages 143-145