{ "item_title" : "Almgren's Big Regularity Paper, Q-Valued Functions Minimizing Dirichlet's Integral and the Regularit", "item_author" : [" Vladimir Scheffer", "Jean E. Taylor "], "item_description" : "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.", "item_img_path" : "https://covers4.booksamillion.com/covers/bam/9/81/024/108/9810241089_b.jpg", "price_data" : { "retail_price" : "350.00", "online_price" : "350.00", "our_price" : "350.00", "club_price" : "350.00", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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