{"product_id":"the-pullback-equation-for-differential-forms-9780817683122","title":"The Pullback Equation for Differential Forms","description":"\u003cp\u003e • Author(s): Gyula Csató\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Birkhauser\u003cbr\u003e • BISAC: Algebra - Linear\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eAn important question in geometry and analysis is to know when two \u003ci\u003ek\u003c\/i\u003e-forms \u003ci\u003ef \u003c\/i\u003eand \u003ci\u003eg\u003c\/i\u003e 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\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\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\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 serve as a valuable reference for researchers or a supplemental text for graduate courses or seminars.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":45274224066711,"sku":"9780817683122","price":9548.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780817683122.webp?v=1769279272","url":"https:\/\/atlanticbooks.com\/products\/the-pullback-equation-for-differential-forms-9780817683122","provider":"Atlantic Books","version":"1.0","type":"link"}