{"product_id":"almgrens-big-regularity-paper-q-valued-vladimir-scheffer-9789810241087","title":"Almgren's Big Regularity Paper, Q-Valued Functions Minimizing Dirichlet's Integral and the Regularit","description":"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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Vladimir Scheffer,Jean E. Taylor\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 9810241089\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9789810241087\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e World Scientific Publishing Company\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 07\/03\/2000\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 972\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 3.94lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 10.08h x 7.09w x 2.14d","brand":"Vladimir Scheffer","offers":[{"title":"Hardcover","offer_id":48448095748351,"sku":"9789810241087","price":350.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_975b8b1c-fe1b-4bff-8bd5-ee80e1c5a5f0.jpg?v=1777236863","url":"https:\/\/www.whiterainbookhouse.com\/products\/almgrens-big-regularity-paper-q-valued-vladimir-scheffer-9789810241087","provider":"WR Book House","version":"1.0","type":"link"}