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Convex integration theory : solutions to the h-principle in geometry and topology

Author: David Spring
Publisher: Basel ; Boston : Birkhäuser Verlag, ©1998.
Series: Monographs in mathematics, v. 92.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

Gromov [17], is one of three general methods in immersion-theoretic topology for solving a broad range of problems in geometry and topology. These general methods are not linearly related in the  Read more...

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Additional Physical Format: Online version:
Spring, David, 1939-
Convex integration theory.
Basel ; Boston : Birkhäuser Verlag, ©1998
(OCoLC)747118462
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: David Spring
ISBN: 376435805X 9783764358051 9780817658052 081765805X 9783034800594 3034800592
OCLC Number: 38048134
Description: viii, 212 pages : illustrations ; 24 cm.
Contents: 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 Degrees-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.
Series Title: Monographs in mathematics, v. 92.
Responsibility: David Spring.
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"Spring's book makes no attempt to include all topics from convex integration theory or to uncover all of the gems in Gromov's fundamental account, but it will nonetheless (or precisely for that Read more...

 
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