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OverviewThere have been many wonderful developments in the theory of minimal surfaces and geometric measure theory in the past 25 to 30 years. Many of the researchers who have produced these excellent results were inspired by this little book-or by Fred Almgren himself. The book is indeed a delightful invitation to the world of variational geometry. A central topic is Plateau's Problem, which is concerned with surfaces that model the behavior of soap films. When trying to resolve the problem, however, one soon finds that smooth surfaces are insufficient: Varifolds are needed. With varifolds, one can obtain geometrically meaningful solutions without having to know in advance all their possible singularities. This new tool makes possible much exciting new analysis and many new results. Plateau's problem and varifolds live in the world of geometric measure theory, where differential geometry and measure theory combine to solve problems which have variational aspects. The author's hope in writing this book was to encourage young mathematicians to study this fascinating subject further. Judging from the success of his students, it achieves this exceedingly well. Full Product DetailsAuthor: Frederick J. AlmgrenPublisher: American Mathematical Society Imprint: American Mathematical Society Edition: UK ed. Volume: No. 13 Weight: 0.122kg ISBN: 9780821827475ISBN 10: 0821827472 Pages: 88 Publication Date: 30 August 2001 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsThe phenomena of least area problems Integration of differential forms over rectifiable sets Varifolds Variational problems involving varifolds References Additional references Index.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |