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" Convex integration theory : "
David Spring.
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BL
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| Record Number
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982852
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b737222
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| Main Entry
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Spring, David,1939-
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| Title & Author
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Convex integration theory : : solutions to the h-principle in geometry and topology /\ David Spring.
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| Publication Statement
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Basel ;Boston :: Birkhäuser Verlag,, ©1998.
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| Series Statement
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Monographs in mathematics ;; vol. 92
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| Page. NO
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viii, 212 pages :: illustrations ;; 24 cm.
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| ISBN
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081765805X
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: 3034800592
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: 376435805X
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: 9780817658052
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: 9783034800594
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: 9783764358051
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081765805X
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| Bibliographies/Indexes
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Includes bibliographical references (pages 207-209) and indexes.
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| Contents
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1. Introduction -- 2. Convex Hulls -- 3. Analytic Theory -- 4. Open Ample Relations in Spaces of 1-Jets -- 5. Microfibrations -- 6. The Geometry of Jet spaces -- 7. Convex Hull Extensions -- 8. Ample Relations -- 9. Systems of Partial Differential Equations -- 10. Relaxation Theorem
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| Abstract
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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. 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.
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| Subject
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Differential topology.
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Differential topology.
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Differential topology.
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Differentialtopologie
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Topologie différentielle.
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| Dewey Classification
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514/.72
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| LC Classification
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QA613.6.S67 1998
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| NLM classification
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cci1icclacc
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coll1lacc
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MAT 285fstub
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SK 350rvk
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