{"product_id":"convex-integration-theory-david-spring-9783764358051","title":"Convex Integration Theory: Solutions to the H-Principle in Geometry and Topology","description":"1. Historical Remarks Convex Integration theory, first introduced by M. Gromov  17], is one of three general methods in immersion-theoretic topology for solving a broad range of problems in geometry and topology. The other methods are: (i) Removal of Singularities, introduced by M. Gromov and Y. Eliashberg  8]; (ii) the covering homotopy method which, following M. Gromov's thesis  16], is also referred to as the method of sheaves. The covering homotopy method is due originally to S. Smale  36] who proved a crucial covering homotopy result in order to solve the classification problem for immersions of spheres in Euclidean space. These general methods are not linearly related in the sense that succes- sive methods subsumed the previous methods. Each method has its own distinct foundation, based on an independent geometrical or analytical insight. Conse- quently, each method has a range of applications to problems in topology that are best suited to its particular insight. For example, a distinguishing feature of Convex Integration theory is that it applies to solve closed relations in jet spaces, including certain general classes of underdetermined non-linear systems of par- tial differential equations. As a case of interest, the Nash-Kuiper Cl-isometrie immersion theorem ean be reformulated and proved using Convex Integration theory (cf. Gromov  18]). No such results on closed relations in jet spaees can be proved by means of the other two methods.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e David Spring\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 376435805X\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783764358051\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Birkhauser\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 12\/18\/1997\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 213\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.24lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.61h x 6.69w x 0.56d","brand":"David Spring","offers":[{"title":"Hardcover","offer_id":44302362673407,"sku":"9783764358051","price":109.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_2db44823-cf8d-423d-9f54-bdc686a4372c.jpg?v=1695161097","url":"https:\/\/www.whiterainbookhouse.com\/products\/convex-integration-theory-david-spring-9783764358051","provider":"WR Book House","version":"1.0","type":"link"}