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Almgren's Big Regularity Paper: Q-Valued Functions Minimizing Dirichlet's Integral and the Regularity of Area-Minimizing Rectifiable Currents Up to Codimension ... Scientific Monograph Series in Mathematics) [Hardcover]

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Item description for Almgren's Big Regularity Paper: Q-Valued Functions Minimizing Dirichlet's Integral and the Regularity of Area-Minimizing Rectifiable Currents Up to Codimension ... Scientific Monograph Series in Mathematics) by Frederick J. Almgren, Jr., Vladimir Scheffer & Jean E. Taylor...

Fred Almgren exploited the excess method for proving regularity theorems in the calculus of variations. His techniques yielded Hlder continuous differentiability except for a small closed singular set. In the sixties and seventies Almgren refined and generalized his methods. Between 1974 and 1984 he wrote a 1,700-page proof that was his most ambitious development of his ground-breaking ideas. Originally, this monograph was available only as a three-volume work of limited circulation. The entire text is faithfully reproduced here.

This book gives a complete proof of the interior regularity of an area-minimizing rectifiable current up to Hausdorff codimension 2. The argument uses the theory of Q-valued functions, which is developed in detail. For example, this work shows how first variation estimates from squash and squeeze deformations yield a monotonicity theorem for the normalized frequency of oscillation of a Q-valued function that minimizes a generalized Dirichlet integral. The principal features of the book include an extension theorem analogous to Kirszbraun's theorem and theorems on the approximation in mass of nearly flat mass-minimizing rectifiable currents by graphs and images of Lipschitz Q-valued functions.



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Item Specifications...


Studio: World Scientific Publishing Company
Pages   955
Est. Packaging Dimensions:   Length: 2" Width: 7" Height: 9.75"
Weight:   3.95 lbs.
Binding  Hardcover
Publisher   World Scientific Publishing Company
ISBN  9810241089  
ISBN13  9789810241087  


Availability  0 units.


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1Books > Subjects > Professional & Technical > Professional Science > Mathematics > Applied > Vector Analysis
2Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Calculus
3Books > Subjects > Science > General
4Books > Subjects > Science > Mathematics > Applied > Vector Analysis
5Books > Subjects > Science > Mathematics > General
6Books > Subjects > Science > Mathematics > Pure Mathematics > Calculus



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Reviews - What do customers think about Almgren's Big Regularity Paper: Q-Valued Functions Minimizing Dirichlet's Integral and the Regularity of Area-Minimizing Rectifiable Currents Up to Codimension ... Scientific Monograph Series in Mathematics)?

Review of Almgren's big regularity paper  Oct 14, 2000
The publication of the Tex formatted version of Almgren's famous big regularity paper makes the original three-volume, 1700 page paper much easier to read. Especially, since Almgren developed the whole new machinery, it takes time for the beginning readers to become familiar with the terminology and to consult essential materials in the Appendix. Readers who have suffered reading the original three hand typed ``telephone books'' will appreciate this all-in-one book.

As in the title of the book, the paper provides a method to deal with the regularity problem of mass minimizing surfaces in higher codimension. This paper not only gives the optimal upper bound of the Hausdorff dimension of the singular sets, but also provides a possible approach to understand the structure of the singular sets of mass minimizing surfaces. This deep but famous paper contains several ingredients to be understood and explored. It is worthwhile for people who are interested in geometric measure theory to spend some time on reading it.

 

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