## ＜電子ブック＞Convex Integration Theory : Solutions to the h-principle in geometry and topology

責任表示 by David Spring Spring, David SpringerLink (Online service) English (英語) Birkhäuser Basel Imprint: Birkhäuser 1998- Basel, Switzerland シリーズ Monographs in Mathematics ; 92 {sect}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 geom...etry 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.続きを見る 1 Introduction{sect}1 Historical Remarks{sect}2 Background Material{sect}3 h-Principles{sect}4 The Approximation Problem2 Convex Hulls{sect}1 Contractible Spaces of Surrounding Loops{sect}2 C-Structures for Relations in Affine Bundles{sect}3 The Integral Representation Theorem3 Analytic Theory{sect}1 The One-Dimensional Theorem{sect}2 The C?-Approximation Theorem4 Open Ample Relations in Spaces of 1-Jets{sect}1 C°-Dense h-Principle{sect}2 Examples5 Microfibrations{sect}1 Introduction{sect}2 C-Structures for Relations over Affine Bundles{sect}3 The C?-Approximation Theorem6 The Geometry of Jet spaces{sect}1 The Manifold X?{sect}2 Principal Decompositions in Jet Spaces7 Convex Hull Extensions{sect}1 The Microfibration Property{sect}2 The h-Stability Theorem8 Ample Relations{sect}1 Short Sections{sect}2 h-Principle for Ample Relations{sect}3 Examples{sect}4 Relative h-Principles9 Systems of Partial Differential Equations{sect}1 Underdetermined Systems{sect}2 Triangular Systems{sect}3 C1-Isometric Immersions10 Relaxation Theorem{sect}1 Filippov's Relaxation Theorem{sect}2 C?-Relaxation TheoremReferencesIndex of Notation.続きを見る Full text available from SpringerLink ebooks - Mathematics and Statistics (Archive)

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レコードID 3204885 QA1-939 510 Mathematics. Mathematics. Mathematics, general. ssj0001296314 9783034898362[3034898363](print) 9783034889407[3034889402] 2020.06.27 2020.06.28