Geometric Measure Theory
eBook - PDF

Geometric Measure Theory

A Beginner's Guide

  1. 154 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Geometric Measure Theory

A Beginner's Guide

About this book

Geometric Measure Theory: A Beginner's Guide provides information pertinent to the development of geometric measure theory. This book presents a few fundamental arguments and a superficial discussion of the regularity theory. Organized into 12 chapters, this book begins with an overview of the purpose and fundamental concepts of geometric measure theory. This text then provides the measure-theoretic foundation, including the definition of Hausdorff measure and covering theory. Other chapters consider the m-dimensional surfaces of geometric measure theory called rectifiable sets and introduce the two basic tools of the regularity theory of area-minimizing surfaces. This book discusses as well the fundamental theorem of geometric measure theory, which guarantees solutions to a wide class of variational problems in general dimensions. The final chapter deals with the basic methods of geometry and analysis in a generality that embraces manifold applications. This book is a valuable resource for graduate students, mathematicians, and research workers.

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Yes, you can access Geometric Measure Theory by Frank Morgan in PDF and/or ePUB format, as well as other popular books in Mathematics & Calculus. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Academic Press
Year
2014
Print ISBN
9780125068550
eBook ISBN
9781483277806
Topic
Mathematics
Subtopic
Calculus
Index
Mathematics

Table of contents

  1. Front Cover
  2. Geometrie Measure Theory: A Beginner's Guide
  3. Copyright Page
  4. Table of Contents
  5. Preface
  6. CHAPTER 1. Geometric Measure Theory
  7. CHAPTER 2. Measures
  8. CHAPTER 3. Lipschitz Functions and Rectifiable Sets
  9. CHAPTER 4. Normal and Rectifiable Currents
  10. CHAPTER 5. The Compactness Theorem and the Existence of Area-Minimizing Surfaces
  11. CHAPTER 6. Examples of Area-Minimizing Surfaces
  12. CHAPTER 7. The Approximation Theorem
  13. CHAPTER 8. Survey of Regularity Results
  14. CHAPTER 9. Monotonicity and Oriented Tangent Cones
  15. CHAPTER 10. The Regularity of Area-Minimizing Hypersurfaces
  16. CHAPTER 11. Flat Chains Modulo v, Varifolds, and (M, ε, δ)-Minimal Sets
  17. CHAPTER 12. Miscellaneous Useful Results
  18. Solutions to Exercises
  19. Bibliography
  20. Index of Symbols
  21. Name Index
  22. Subject Index