» » Almgren's Big Regularity Paper

Information of news
7-01-2015, 18:58

Almgren's Big Regularity Paper

Category: E-Books

Almgren's Big Regularity Paper

Vladimir Scheffer, Jean E. Taylor, "Almgren's Big Regularity Paper: Q-valued Functions Minimizing Dirichlet's Integral and the Regularity of Area-minimizing Rectifiable Currents Up to"
2000 | ISBN-10: 9810241089 | 972 pages | PDF | 31 MB

Fred Almgren created the excess method for proving regularity theorems in the calculus of variations. His techniques yielded Holder continuity 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 exposition 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.

Links are Interchangeable - No Password





Site BBcode/HTML Code:

Tags to an Article: Almgren, Big, Regularity, Paper

Dear visitor, you went to the site as unregistered user.
We recommend you Sign up or Login to website under your name.
Would you like to leave your comment? Please Login to your account to leave comments. Don't have an account? You can create a free account now.