Almgren's big regularity paper : Q-valued functions minimizing Dirichlet's integral and the regularity of area-minimizing rectifiable currents up to codimension 2 /
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| Imprint: | Singapore ; River Edge, NJ : World Scientific, c2000. |
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| Description: | xv, 955 p. : ill. ; 26 cm. |
| Language: | English |
| Series: | World scientific monograph series in mathematics ; vol. 1 World scientific monograph series in mathematics ; v. 1. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4318343 |
| Summary: | Fred Almgren exploited the excess method for proving regularity theorems in the calculus of variations. His techniques yielded H lder 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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| Physical Description: | xv, 955 p. : ill. ; 26 cm. |
| Bibliography: | Includes bibliographical references (p. 953-955). |
| ISBN: | 9810241089 |
