Geometric Measure Theory

A Beginner's Guide

Inbunden, Engelska, 2016

1 139 kr

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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 Poincar� conjecture, and new topical coverage of manifolds taking into account all recent research advances in theory and applications.

Focuses on core geometry rather than proofs, paving the way to fast and efficient insight into an extremely complex topic in geometric structures
Enables further study of more advanced topics and texts
Demonstrates in the simplest possible way how to relate concepts of geometric analysis by way of algebraic or topological techniques
Contains full topical coverage of The Log-Convex Density Conjecture
Comprehensively updated throughout

Produktinformation

Utgivningsdatum2016-04-07
Mått152 x 229 x 19 mm
Vikt610 g
FormatInbunden
SpråkEngelska
Antal sidor272
Upplaga5
FörlagElsevier Science
ISBN9780128044896

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Beräkning och matematisk analys inom Naturvetenskap och teknik

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.

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 Poincaré Conjecture19. Double Bubbles in Spheres, Gauss Space, and Tori20. The Log-Convex Density Conjecture21. Solutions to Exercises

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Werner G. K. Stritzke, Stephan Lewandowsky, David Denemark, Joseph Clare, Frank Morgan, Perth) Stritzke, Werner G. K. (University of Western Australia, Perth) Lewandowsky, Stephan (University of Western Australia, Perth) Denemark, David (University of Western Australia, Perth) Clare, Joseph (University of Western Australia, Perth) Morgan, Frank (University of Western Australia

Inbunden

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