Abstract
The theory in Part I proves the h-principle for open ample relations \({\rm R } \subset {X}^{{\rm (1)}}\). In general however, the theory in Part I does not extend naturally to prove the h-principle for open, ample relations \({\rm R } \subset {X}^{{\rm (r)}}\) in case \({r} \ge {\rm 2}{\rm}\). In effect, the analytic theory in Chapter III allows for controlled “large” moves in the pure derivatives \(\partial ^{\rm r} / \partial t^r\) while maintaining small perturbations in all the complementary \( \bot\)-derivatives. This analytic technique works well in spaces of 1-jets \({X}^{{\rm (1)}}\) since in local coordinates first order derivatives are all pure.
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© 1998 Birkhäuser Verlag
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Spring, D. (1998). Microfibrations. In: Convex Integration Theory. Modern Birkhäuser Classics. Springer, Basel. https://doi.org/10.1007/978-3-0348-0060-0_5
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DOI: https://doi.org/10.1007/978-3-0348-0060-0_5
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