Geometric Measure Theory: A Beginner's Guide

Geometric Measure Theory: A Beginner's Guide

by Frank Morgan

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Product Details

ISBN-13: 9780080525600
Publisher: Elsevier Science
Publication date: 08/22/2000
Sold by: Barnes & Noble
Format: NOOK Book
Pages: 227
File size: 10 MB

About the Author

Frank Morgan is the Dennis Meenan '54 Third Century Professor of Mathematics at Williams College. He obtained his B.S. from MIT and his M.S. and Ph.D. from Princeton University. His research interest lies in minimal surfaces, studying the behavior and structure of minimizers in various settings. He has also written Riemannian Geometry: A Beginner's Guide, Calculus Lite, and most recently The Math Chat Book, based on his television program and column on the Mathematical Association of America Web site.

Table of Contents

1. Geometric Measure Theory 2. Measures 3. Lipschitz Functions and Rectifiable Sets 4. Normal and Rectifiable Currents 5. The Compactness Theorem and the Existence of Area-Minimizing Surfaces 6. Examples of Area-Minimizing Surfaces 7. The Approximation Theorem 8. Survey of Regularity Results 9. Monotonicity and Oriented Tangent Cones 10. The Regularity of Area-Minimizing Hypersurfaces 11. Flat Chains Modulo v, Varifolds, and (M,E,)-Minimal Sets 12. Miscellaneous Useful Results 13. Soap Bubble Clusters 14. Proof of Double Bubble Conjecture 15. The Hexagonal Honeycomb and Kelvin Conjectures 16. Immiscible Fluids and Crystals 17. Isoperimetric Theorems in General Codimension 18. Manifolds with Density and Perelman's Proof of the Poincaré Conjecture 19. Double Bubbles in Spheres, Gauss Space, and Tori 20. The Log-Convex Density Conjecture 21. Solutions to Exercises

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