Convex Integration Theory - Solutions to the h-principle in geometry and topology

de Springer Basel
État : Neuf
113,82 €
TVA incluse - Livraison GRATUITE
Springer Basel Convex Integration Theory - Solutions to the h-principle in geometry and topology
Springer Basel - Convex Integration Theory - Solutions to the h-principle in geometry and topology

Ce produit vous plaît ? N'hésitez pas à le dire !

113,82 € dont de TVA
Plus que 1 exemplaire(s) disponible(s) Plus que 1 exemplaire(s) disponible(s)
Livraison : entre jeudi 26 mai 2022 et lundi 30 mai 2022
Vente et expédition: Dodax

La 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.

Détails du produit

Commentaire illustrations:
VIII, 213 p. 2 illus.
Table des Matières:
1 Introduction.- §1 Historical Remarks.- §2 Background Material.- §3 h-Principles.- §4 The Approximation Problem.- 2 Convex Hulls.- §1 Contractible Spaces of Surrounding Loops.- §2 C-Structures for Relations in Affine Bundles.- §3 The Integral Representation Theorem.- 3 Analytic Theory.- §1 The One-Dimensional Theorem.- §2 The C?-Approximation Theorem.- 4 Open Ample Relations in Spaces of 1-Jets.- §1 C°-Dense h-Principle.- §2 Examples.- 5 Microfibrations.- §1 Introduction.- §2 C-Structures for Relations over Affine Bundles.- §3 The C?-Approximation Theorem.- 6 The Geometry of Jet spaces.- §1 The Manifold X?.- §2 Principal Decompositions in Jet Spaces.- 7 Convex Hull Extensions.- §1 The Microfibration Property.- §2 The h-Stability Theorem.- 8 Ample Relations.- §1 Short Sections.- §2 h-Principle for Ample Relations.- §3 Examples.- §4 Relative h-Principles.- 9 Systems of Partial Differential Equations.- §1 Underdetermined Systems.- §2 Triangular Systems.- §3 C1-Isometric Immersions.- 10 Relaxation Theorem.- §1 Filippov’s Relaxation Theorem.- §2 C?-Relaxation Theorem.- References.- Index of Notation.
Spring, David;Spring
Type de média:
Couverture rigide
Springer Basel
Nombre de pages:

Données de base

Type d'produit:
Livre relié
Date de publication:
18 décembre 1997
Dimensions du colis:
0.234 x 0.155 x 0.018 m; 0.499 kg
113,82 €
Nous avons recours aux cookies sur notre site internet afin de rendre votre visite plus agréable et ergonomique. Nous vous invitons ainsi à cliquer sur "Accepter les cookies" ! De plus amples informations sont disponibles dans notreDéclaration de protection des données.