Geometric measure theory : a beginner's guide
著者
書誌事項
Geometric measure theory : a beginner's guide
Academic Press is an imprint of Elsevier, c2016
5th ed
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注記
Includes bibliographical references (p. 235-254) and indexes
内容説明・目次
内容説明
Geometric Measure Theory: A Beginner's Guide, Fifth Edition provides the framework readers need to understand the structure of a crystal, a soap bubble cluster, or a universe.
The book is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Brevity, clarity, and scope make this classic book an excellent introduction to more complex ideas from geometric measure theory and the calculus of variations for beginning graduate students and researchers.
Morgan emphasizes geometry over proofs and technicalities, providing a fast and efficient insight into many aspects of the subject, with new coverage to this edition including topical coverage of the Log Convex Density Conjecture, a major new theorem at the center of an area of mathematics that has exploded since its appearance in Perelman's proof of the Poincare conjecture, and new topical coverage of manifolds taking into account all recent research advances in theory and applications.
目次
1. Geometric Measure Theory2. Measures3. Lipschitz Functions and Rectifiable Sets4. Normal and Rectifiable Currents5. The Compactness Theorem and the Existence of Area-Minimizing Surfaces6. Examples of Area-Minimizing Surfaces7. The Approximation Theorem8. Survey of Regularity Results9. Monotonicity and Oriented Tangent Cones10. The Regularity of Area-Minimizing Hypersurfaces11. Flat Chains Modulo v, Varifolds, and (M,E,)-Minimal Sets12. Miscellaneous Useful Results13. Soap Bubble Clusters14. Proof of Double Bubble Conjecture15. The Hexagonal Honeycomb and Kelvin Conjectures16. Immiscible Fluids and Crystals17. Isoperimetric Theorems in General Codimension18. Manifolds with Density and Perelman's Proof of the Poincare Conjecture19. Double Bubbles in Spheres, Gauss Space, and Tori20. The Log-Convex Density Conjecture21. Solutions to Exercises
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