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【转贴】Geometric Measure Theory: A Beginner's Guide
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Geometric Measure Theory: A Beginner's Guide Publisher: Academic Press Number Of Pages: 226 Publication Date: 2000-07-24 Sales Rank: 762232 ISBN / ASIN: 0125068514 EAN: 9780125068512 Binding: Hardcover Manufacturer: Academic Press Studio: Academic Press Average Rating: 5 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. Review: Up-to-date reference. This thin book (175 pages) provides the newcomer or graduate student with an illustrated introduction to geometric measure theory: the basic ideas, terminology, and results. The author has included a few fundamental arguments and a superficial discussion of the regularity theory, but his goal is merely to introduce the subject and make the standard text, "Geometric Measure Theory" by Federer, more accesible. This second edition includes updated material and references, corrections, and a new chapter on soap bubble clusters. Its contents are: Measures, Lipschitz functions and rectifiable sets, normal and rectifiable currents, the completeness theorem, area-minimizing surfaces, the approximation theorem, regualrity results, monotonicity and oriented tanget cones, flat chains, varifolds, minimal sets, soap bubble clusters. Includes excercises, plenty of illustrations, and extensive references. Highly useful for advanced undergraduate and graduate students in analysis and geometry. The "next step" for fractal geometers. If you want to buy it maybe it should be better to wait for the third edition to appear by June 2000. http://rapidshare.com/files/42101439/geometric.measure.theory.rar [ Last edited by laizuliang on 2007-10-31 at 16:26 ] |
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