Convex Integration Theory: Solutions to the H-Principle in Geometry and Topology (Hardcover, 1998)

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.