no. 1
Applications of convex integration to symplectic and contact geometry
Annales de l'Institut Fourier, Tome 37 (1987) no. 1, pp. 107-133.

La méthode d’intégration convexe développée par Gromov est appliquée aux problèmes concernant l’existence et l’unicité des structures symplectiques et de contact

We apply Gromov’s method of convex integration to problems related to the existence and uniqueness of symplectic and contact structures

@article{AIF_1987__37_1_107_0,
     author = {Duff, Dusa Mc},
     title = {Applications of convex integration to symplectic and contact geometry},
     journal = {Annales de l'Institut Fourier},
     pages = {107--133},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {37},
     number = {1},
     year = {1987},
     doi = {10.5802/aif.1079},
     mrnumber = {88i:58057},
     zbl = {0572.58010},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1079/}
}
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Duff, Dusa Mc. Applications of convex integration to symplectic and contact geometry. Annales de l'Institut Fourier, Tome 37 (1987) no. 1, pp. 107-133. doi : 10.5802/aif.1079. http://www.numdam.org/articles/10.5802/aif.1079/

[B] D. Bennequin, Entrelacements et équations de Pfaff, Astérisque, 107-108 (1983), 87-161. | Numdam | MR | Zbl

[C] E. Cartan, Les systèmes différentiels extérieurs et leurs applications géométriques, Herman, Paris (1945). | MR | Zbl

[E] J. Eliashberg, Rigidity of symplectic and contact structures, Preprint, 1981.

[GS] R. Greene and K. Shiohama, Diffeomorphisms and volume-preserving embeddings of non-compact manifolds, TAMS, 225 (1979), 403-414. | MR | Zbl

[G1] M. Gromov, Stable mappings of foliations into manifolds, Izv. Akad. Nauk SSR, Mat, 33 (1969), 707-734. | MR | Zbl

[G2] M. Gromov, Convex integration of differential relations I, Math USSR Izv., 7 (1973), 329-343. | MR | Zbl

[G3] M. Gromov, Partial Differential Relations, Springer Verlag, to appear. | MR | Zbl

[G4] M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math., 82 (1985), 307-347. | EuDML | MR | Zbl

[H1] A. Haefliger, Feuilletages sur les variétés ouvertes, Topology, 9 (1970), 183-194. | MR | Zbl

[H2] A. Haefliger, Homotopy and integrability, Manifolds-Amsterdam, Springer Lecture Notes # 197 (1971) 133-163. | MR | Zbl

[H3] A. Haefliger, Lectures on the theorem of Gromov, Springer Lecture Notes # 209, (1971), 128-141. | MR | Zbl

[M] J. Martinet, Formes de contact sur les variétés de dimension 3, Springer Lecture Notes # 209, (1971), 128-163. | MR | Zbl

[MD1] D. Mcduff, On groups of volume-preserving diffeomorphisms and foliations with transverse volume form, Proc. London Math. Soc., 43 (1981), 295-320. | MR | Zbl

[MD2] D. Mcduff, Local homology of groups of volume-preserving diffeomorphisms, I, Ann. Sci. Ec. Norm. Sup., 15 (1982), 609-648. | Numdam | MR | Zbl

[MD3] D. Mcduff, Some canonical cohomology classes on groups of volume-preserving diffeomorphisms, TAMS, 275 (1983), 345-356. | MR | Zbl

[MD4] D. Mcduff, Examples of simply connected symplectic non-Kählerian manifolds, J. Diff. Geom., 20 (1984), 27. | MR | Zbl

[MD5] D. Mcduff, Examples of symplectic structures, to appear in Invent. Math. | Zbl

[Me] C. Meckert, Formes de contact sur la somme connexe de deux variétés de contact, Ann. Inst. Fourier, Grenoble, 32-3 (1982), 251-260. | Numdam | MR | Zbl

[Mo] J. Moser, On the volume elements on a manifolds, TAMS, 120 (1965), 286-294. | MR | Zbl

[Sp] D. Spring, Convex integration of non-linear system of partial differential equations, Ann. Inst. Fourier, Grenoble, 33-3 (1983) 121-177. | Numdam | MR | Zbl

[S] D. Sullivan, Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math., 36 (1976), 225-255. | MR | Zbl

[To] C. Thomas, A classifying space for the contact pseudogroup, Mathematika, 25 (1978), 191-201. | MR | Zbl

[T] W. Thurston, Some simple examples of symplectic manifolds, Proc. AMS, 55 (1976), 467-468. | MR | Zbl

[TW] W. Thurston and H. Winkelnkemper, On the existence of contact forms, Proc. AMS, 52 (1975), 345-347. | MR | Zbl

[V] C. Viterbo, A Proof of Weinstein's conjecture in R2n, preprint, 1986. | Numdam | Zbl

[W] A. Weinstein, On the hypotheses of Rabinowitz's periodic orbit theorems, J. Diff. Eq., 33 (1979), 353-358. | MR | Zbl

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