Author | Spring, David. author |
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Title | Convex Integration Theory [electronic resource] : Solutions to the h-principle in geometry and topology / by David Spring |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1998 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8940-7 |
Descript | VIII, 213 p. 2 illus. online resource |
1 Introduction -- ยง1 Historical Remarks -- ยง2 Background Material -- ยง3 h-Principles -- ยง4 The Approximation Problem -- 2 Convex Hulls -- ยง1 Contractible Spaces of Surrounding Loops -- ยง2 C-Structures for Relations in Affine Bundles -- ยง3 The Integral Representation Theorem -- 3 Analytic Theory -- ยง1 The One-Dimensional Theorem -- ยง2 The C?-Approximation Theorem -- 4 Open Ample Relations in Spaces of 1-Jets -- ยง1 Cยฐ-Dense h-Principle -- ยง2 Examples -- 5 Microfibrations -- ยง1 Introduction -- ยง2 C-Structures for Relations over Affine Bundles -- ยง3 The C?-Approximation Theorem -- 6 The Geometry of Jet spaces -- ยง1 The Manifold X? -- ยง2 Principal Decompositions in Jet Spaces -- 7 Convex Hull Extensions -- ยง1 The Microfibration Property -- ยง2 The h-Stability Theorem -- 8 Ample Relations -- ยง1 Short Sections -- ยง2 h-Principle for Ample Relations -- ยง3 Examples -- ยง4 Relative h-Principles -- 9 Systems of Partial Differential Equations -- ยง1 Underdetermined Systems -- ยง2 Triangular Systems -- ยง3 C1-Isometric Immersions -- 10 Relaxation Theorem -- ยง1 Filippovโs Relaxation Theorem -- ยง2 C?-Relaxation Theorem -- References -- Index of Notation