Almgren's Big Regularity Paper, Q-valued Functions Minimizing Dirichlet's Integral And The Regularit

Almgren's Big Regularity Paper, Q-valued Functions Minimizing Dirichlet's Integral And The Regularit
Author :
Publisher : World Scientific
Total Pages : 973
Release :
ISBN-10 : 9789814494113
ISBN-13 : 9814494119
Rating : 4/5 (119 Downloads)

Book Synopsis Almgren's Big Regularity Paper, Q-valued Functions Minimizing Dirichlet's Integral And The Regularit by : Vladimir Scheffer

Download or read book Almgren's Big Regularity Paper, Q-valued Functions Minimizing Dirichlet's Integral And The Regularit written by Vladimir Scheffer and published by World Scientific. This book was released on 2000-06-30 with total page 973 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fred Almgren exploited the excess method for proving regularity theorems in the calculus of variations. His techniques yielded Hölder 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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