Geometric Measure Theory
eBook - ePub

Geometric Measure Theory

A Beginner's Guide

  1. 227 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Geometric Measure Theory

A Beginner's Guide

Book details
Table of contents
Citations

About This Book

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.

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Information

Publisher
Academic Press
Year
2000
ISBN
9780080525600
Edition
3
Topic
Mathematics
Subtopic
Applied Mathematics
Index
Mathematics

Table of contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Dedication
  5. Copyright
  6. Preface
  7. Chapter 1: Geometric Measure Theory
  8. Chapter 2: Measures
  9. Chapter 3: Lipschitz Functions and Rectifiable Sets
  10. Chapter 4: Normal and Rectifiable Currents
  11. Chapter 5: The Compactness Theorem and the Existence of Area-Minimizing Surfaces
  12. Chapter 6: Examples of Area-Minimizing Surfaces
  13. Chapter 7: The Approximation Theorem
  14. Chapter 8: Survey of Regularity Results
  15. Chapter 9: Monotonicity and Oriented Tangent Cones
  16. Chapter 10: The Regularity of Area-Minimizing Hypersurfaces
  17. Chapter 11: Flat Chains Modulo v, Varifolds, and (M, ξ, δ)-Minimal Sets
  18. Chapter 12: Miscellaneous Useful Results
  19. Chapter 13: Soap Bubble Clusters
  20. Chapter 14: Proof of Double Bubble Conjecture
  21. Chapter 15: The Hexagonal Honeycomb and Kelvin Conjectures
  22. Chapter 16: Immiscible Fluids and Crystals
  23. Chapter 17: Isoperimetric Theorems in General Codimension
  24. Solutions to Exercises
  25. Bibliography
  26. Index of Symbols
  27. Name Index
  28. Subject Index
  29. Inside Back Cover