{"product_id":"the-pullback-equation-for-differential-gyula-csatze-9780817683122","title":"The Pullback Equation for Differential Forms","description":"\u003cp\u003eAn important question in geometry and analysis is to know when two \u003ci\u003ek\u003c\/i\u003e-forms \u003ci\u003ef \u003c\/i\u003eand g are equivalent through a change of variables. The problem is therefore to find a map \u003ci\u003eφ \u003c\/i\u003eso that it satisfies the pullback equation: \u003ci\u003eφ\u003c\/i\u003e\u003ci\u003e*\u003c\/i\u003e(\u003ci\u003eg\u003c\/i\u003e) = \u003ci\u003ef\u003c\/i\u003e.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eIn more physical terms, the question under consideration can be seen as a problem of mass transportation. The problem has received considerable attention in the cases \u003ci\u003ek \u003c\/i\u003e= 2 and \u003ci\u003ek \u003c\/i\u003e= \u003ci\u003en\u003c\/i\u003e, but much less when 3 k n-1. The present monograph provides the first comprehensive study of the equation.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe work begins by recounting various properties of exterior forms and differential forms that prove useful throughout the book. From there it goes on to present the classical Hodge-Morrey decomposition and to give several versions of the Poincaré lemma. The core of the book discusses the case \u003ci\u003ek \u003c\/i\u003e= \u003ci\u003en\u003c\/i\u003e, and then the case 1k n-1 with special attention on the case \u003ci\u003ek \u003c\/i\u003e= 2, which is fundamental in symplectic geometry. Special emphasis is given to optimal regularity, global results and boundary data. The last part of the work discusses Hölder spaces in detail; all the results presented here are essentially classical, but cannot be found in a single book. This section may serve as a reference on Hölder spaces and therefore will be useful to mathematicians well beyond those who are only interested in the pullback equation.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003ci\u003eThe Pullback Equation for Differential Forms \u003c\/i\u003eis a self-contained and concise monograph intended for both geometers and analysts. The book may serveas a valuable reference for researchers or a supplemental text for graduate courses or seminars.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Gyula Csató, Bernard Dacorogna, Olivier Kneuss\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0817683127\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780817683122\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Birkhauser\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 11\/12\/2011\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 436\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.77lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 1.00d","brand":"Gyula Csató","offers":[{"title":"Hardcover","offer_id":47202678997247,"sku":"9780817683122","price":139.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_26eab53e-e4f5-460b-8967-7532654c02e1.jpg?v=1756833082","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-pullback-equation-for-differential-gyula-csatze-9780817683122","provider":"WR Book House","version":"1.0","type":"link"}