{ "item_title" : "Convex Integration Theory", "item_author" : [" David Spring "], "item_description" : " 1. Historical Remarks Convex Integration theory, first introduced by M. Gromov17], 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. Eliashberg8]; (ii) the covering homotopy method which, following M. Gromov's thesis16], is also referred to as the method of sheaves. The covering homotopy method is due originally to S. Smale36] 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. Gromov18]). No such results on closed relations in jet spaees can be proved by means of the other two methods.", "item_img_path" : "https://covers4.booksamillion.com/covers/bam/3/76/435/805/376435805X_b.jpg", "price_data" : { "retail_price" : "109.99", "online_price" : "109.99", "our_price" : "109.99", "club_price" : "109.99", "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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