Introduction to the h-Principle

By Y. Eliashberg, N. Mishachev. 2002

450 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/601f541c6369c58547f1f51488a0696860b7257b

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Citations in the corpus

Milnor open books and Milnor fillable contact 3-manifolds (2004, methodology): “) Now, using Gray’s theorem (see [6] for instance), it is easy to prove:”
h -Principle and Rigidity for C 1, α Isometric Embeddings (2012, methodology): “This technique was developed by Gromov [15, 16] into a very powerful tool to prove the h-principle in a wide variety of geometric problems (see also [12, 33]).”
Symplectic embedding problems, old and new (2017, background): “Symplectic embeddings of domains into manifolds of larger dimensions are also flexible [36, 47].”
h-Principles for the Incompressible Euler Equations (2012, background): “Nash’s idea has been further developed by Kuiper, Gromov, and others, and falls nowadays under the name of convex integration, see [11,12,16,27].”
Topological methods in moduli theory (2014, background): “Another very interesting topic is Gromov’s h-principle, for which we refer the reader to [152], and [74].”
Geometric criteria for overtwistedness (2015, background): “ which is satised by loose Legendrians, but not by all Legendrians, will be most useful for us. It constitutes the characterizing property of loose Legendrians, and as a basic form of an h{principle [26] it indicates that this class of Legendrians is related to the exible side of contact topology. T”
Existence of Engel structures (2004, methodology): “For open manifolds, Theorem 1.2 can be proved using the h{principle for open, Di{ invariant relations, cf. [ ElM ].”
Zoll Manifolds and Complex Surfaces (2002, background): “The first author would like to thank Denny Hill, Dusa McDuff, and Dennis Sullivan for helpful conversations, as well as Bob Gompf and Yasha Eliashberg for some helpful e-mail.”
Dissipative continuous Euler flows (2012, unknown): “[10]).”
A biased view of symplectic cohomology (2007, background): “3, 18]. Clearly, such a manifold cannot be decomposed into Weinstein handles. Attachment of k-handles with k<n= 1 2dimMis an essentially topological process, since it is governed by an h-principle [12]. On the side of pseudo-holomorphic curve theory, this is reﬂected by a remarkable result of Cie”
Lectures on Holomorphic Curves in Symplectic and Contact Geometry (2010, unknown): “[EM02] or [Gei03].”
Noncritical holomorphic functions on Stein manifolds (2002, methodology): “bian satisﬁes the condition Jh(x)·Ax ∈ GLq(C). We see as in Lemma 6.5 above that Ω is ample in the coordinate directions. Hence Gromov’s convex integration lemma from [Gro2, 2.4.1.] (or Sect. 18.2 in [EM]) gives a smooth extension of fe across the handle Esuch that x→ Jfe(x)·Ax ∈ GLq(C) is homotopic”