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Convex Integration Theory: Solutions to the H-Principle in Geometry and Topology - Couverture rigide
Synopsis
§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.
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- ÉditeurBirkhauser Verlag AG
- Date d'édition1997
- ISBN 10 376435805X
- ISBN 13 9783764358051
- ReliureRelié
- Langueanglais
- Nombre de pages213
- ÉditeurSpring David
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Convex integration theory. Solutions to the h-principle in geometry and topology.
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Basel, Birkhäuser, 2011
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Couverture rigide
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Convex Integration Theory: Solutions to the h-principle in geometry and topology (Monographs in Mathematics, 92)
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Birkh�user, 1997
ISBN 10 : 376435805X
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Ancien ou d'occasion
Couverture rigide
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Convex Integration Theory
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Convex Integration Theory
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Convex Integration Theory
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Convex Integration Theory - Solutions To The H-principle In Geometry And Topology (monographs In Mathematics)
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Convex Integration Theory - Solutions To The H-principle In Geometry And Topology (monographs In Mathematics)
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Convex Integration Theory
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Birkhäuser Basel, 1997
ISBN 10 : 376435805X
ISBN 13 : 9783764358051
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Couverture rigide
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Convex Integration Theory : Solutions to the h-principle in geometry and topology
Edité par
Birkhäuser Basel, 1997
ISBN 10 : 376435805X
ISBN 13 : 9783764358051
Neuf
Couverture rigide
Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne
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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - This book provides a comprehensive study of convex integration theory in immersion-theoretic topology. Convex integration theory, developed originally by M. Gromov, provides general topological methods for solving the h-principle for a wide variety of problems in differential geometry and topology, with applications also to PDE theory and to optimal control theory. Though topological in nature, the theory is based on a precise analytical approximation result for higher order derivatives of functions, proved by M. Gromov. This book is the first to present an exacting record and exposition of all of the basic concepts and technical results of convex integration theory in higher order jet spaces, including the theory of iterated convex hull extensions and the theory of relative h-principles. A second feature of the book is its detailed presentation of applications of the general theory to topics in symplectic topology, divergence free vector fields on 3-manifolds, isometric immersions, totally real embeddings, underdetermined non-linear systems of PDEs, the relaxation theorem in optimal control theory, as well as applications to the traditional immersion-theoretical topics such as immersions, submersions, k-mersions and free maps. The book should prove useful to graduate students and to researchers in topology, PDE theory and optimal control theory who wish to understand the h-principle and how it can be applied to solve problems in their respective disciplines. N° de réf. du vendeur 9783764358051
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Convex Integration Theory
Edité par
Birkhäuser Basel, Birkhäuser Basel Dez 1997, 1997
ISBN 10 : 376435805X
ISBN 13 : 9783764358051
Neuf
Couverture rigide
Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book provides a comprehensive study of convex integration theory in immersion-theoretic topology. Convex integration theory, developed originally by M. Gromov, provides general topological methods for solving the h-principle for a wide variety of problems in differential geometry and topology, with applications also to PDE theory and to optimal control theory. Though topological in nature, the theory is based on a precise analytical approximation result for higher order derivatives of functions, proved by M. Gromov. This book is the first to present an exacting record and exposition of all of the basic concepts and technical results of convex integration theory in higher order jet spaces, including the theory of iterated convex hull extensions and the theory of relative h-principles. A second feature of the book is its detailed presentation of applications of the general theory to topics in symplectic topology, divergence free vector fields on 3-manifolds, isometric immersions, totally real embeddings, underdetermined non-linear systems of PDEs, the relaxation theorem in optimal control theory, as well as applications to the traditional immersion-theoretical topics such as immersions, submersions, k-mersions and free maps. The book should prove useful to graduate students and to researchers in topology, PDE theory and optimal control theory who wish to understand the h-principle and how it can be applied to solve problems in their respective disciplines. 228 pp. Englisch. N° de réf. du vendeur 9783764358051
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