Orbites périodiques et courbes pseudo-holomorphes. Application à la conjecture de Weinstein en dimension 3
Séminaire Bourbaki : volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Talk no. 786, p. 309-333
@incollection{SB_1993-1994__36__309_0,
     author = {Laudenbach, Fran\c cois},
     title = {Orbites p\'eriodiques et courbes pseudo-holomorphes. Application \`a la conjecture de Weinstein en dimension $3$},
     booktitle = {S\'eminaire Bourbaki : volume 1993/94, expos\'es 775-789},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {227},
     year = {1995},
     note = {talk:786},
     pages = {309-333},
     zbl = {0853.57013},
     mrnumber = {1321652},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1993-1994__36__309_0}
}
Laudenbach, François. Orbites périodiques et courbes pseudo-holomorphes. Application à la conjecture de Weinstein en dimension $3$, in Séminaire Bourbaki : volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Talk no. 786, pp. 309-333. http://www.numdam.org/item/SB_1993-1994__36__309_0/

[AL] M. Audin, J. Lafontaine, eds., Holomorphic curves in symplectic geometry, Birkhäuser, 1994. | MR 1274923 | Zbl 0802.53001

[Be1] D. Bennequin, Entrelacements et équations de Pfaff, Astérisque 103-108 (1983), 83-161. | Numdam | MR 753131 | Zbl 0573.58022

[Be2] D. Bennequin, Caustique mystique [d'après Arnold et al.], Sém. Bourbaki, Astérisque 133-134 (1986), 19-56. | Numdam | MR 837213 | Zbl 0632.58011

[Be3] D. Bennequin, Problèmes elliptiques, surfaces de Riemann et structures symplectiques [d'après M. Gromov], Sém. Bourbaki, Astérisque 145- 146 (1987), 111-136. | Numdam | MR 880029 | Zbl 0644.53031

[BG] E. Bedford, B. Gaveau, Envelopes of holomorphy of certain 2 -spheres in 𝐂 2 , Amer. J. of Math. 105 (1983), 975-1009. | Article | MR 708370 | Zbl 0535.32008

[Ber] H. Berestycki, Solutions périodiques de systèmes hamiltoniens, Sém. Bourbaki, Astérisque 105-106 (1983), 105-128. | Numdam | MR 728984 | Zbl 0526.58016

[Bers] L. Bers, An outline of the theory of pseudo-analytic functions, Bull. Amer. Math. Soc. 62 (1956), 291-331. | MR 81936 | Zbl 0072.07703

[Bi] E. Bishop, Differentiable manifolds in complex Euclidian space, Duke Math. J. | MR 200476 | Zbl 0154.08501

[El1] Y. Eliashberg, Classification of overtwisted contact structures on 3- manifolds, Invent. Math. 98 (1989), 623-637. | MR 1022310 | Zbl 0684.57012

[El2] Y. Eliashberg, Filling by holomorphic discs and its applications, London Math. Soc. Lect. Notes Ser. 151 (1991), 45-67. | MR 1171908 | Zbl 0731.53036

[El3] Y. Eliashberg, Contact 3-manifolds, twenty years since J. Martinet's work, Ann. Inst. Fourier 42 (1992), 165-192. | Numdam | MR 1162559 | Zbl 0756.53017

[Ga] P. Gauduchon, The canonical almost complex structure on the manifold of 1-jets of pseudo-holomorphic mappings between two almost complex manidolds, p. 69-74 in [AL].

[Gi1] E. Giroux, Convexité en topologie de contact, Comment. Math. Helv. 66 (1991), 637-677. | MR 1129802 | Zbl 0766.53028

[Gi2] E. Giroux, Topologie de contact en dimension trois [autour de travaux de Yakov Eliashberg], Sém. Bourbaki, Astérisque 216 (1993), 7-34. | Numdam | MR 1246390 | Zbl 0793.53037

[Gr] M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. math. 82 (1985), 307-347. | MR 1554036 | Zbl 0592.53025

[Hed] G. Hedlund, Fuchsian groups and transitive horocycles, Duke Math. Journal 2 (1936), 530-542. | JFM 62.0392.03 | MR 1545946

[Hem] J. Hempel, 3-manifolds, Annals of Math. Studies, Princeton Univ. Press, 1976. | MR 415619 | Zbl 0345.57001

[Her] M. Herman, Exemples de flots hamiltoniens dont aucune perturbation en topologie C n'a d'orbites périodiques sur un ouvert de surfaces d'énergie, C. R. Acad. Sc. Paris série I Math. 312 (1991), 989-994. | Zbl 0759.58016

[Ho] H. Hofer, Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three, Invent. Math. 114 (1993), 515-563. | MR 1244912 | Zbl 0797.58023

[HV] H. Hofer, C. Viterbo, The Weinstein conjecture in the presence of holomorphic spheres, Comm. Pure Appl. Math. 45 (1992), 583-622. | MR 1162367 | Zbl 0773.58021

[HW] H. Hofer, K. Wysocki, communication orale.

[Lab] F. Labourie, communication orale.

[LF] L. Lusternik, A. Fet, Variational problems on closed manifolds, Dokl. Akad. Nauk SSSR 81 (1951), 17-18. | MR 44760 | Zbl 0045.20903

[Ma] J. Martinet, Formes de contact sur les variétés de dimension trois, p. 142-163 in Proceedings of Liverpool Singularities Symposium II, L.N.M. 209, Springer, 1971. | MR 350771 | Zbl 0215.23003

[Mc1] D. Mcduff, The structure of rational and ruled symplectic 4-manifolds, J. of AMS 3 (1990), 672-712. | MR 1049697 | Zbl 0723.53019

[Mc2] D. Mcduff, The local behaviour of holomorphic curves in almost complex 4-manifolds, J. of Diff. Geo. 34 (1991), 143-164. | MR 1114456 | Zbl 0736.53038

[Mc3] D. Mcduff, Symplectic manifolds with contact type boundaries, Invent. math. 103 (1991), 651-671. | MR 1091622 | Zbl 0719.53015

[Mc4] D. Mcduff, Singularities and positivity of intersections of J-holomorphic curves, p. 191-215 in [AL]. | MR 1274930

[Mi] J. Milnor, On the 3 -dimensional Brieskorn manifolds M ( p , q , r ) , p. 175-225 in : Knots, groups and 3 -manifolds, (papers dedicated to the memory of R.H. Fox, ed. by L. Neuwirth, Annals of Math. Studies 84, Princeton Univ. Press, 1975. | MR 418127 | Zbl 0305.57003

[Mu] M.-P. Muller, Gromov's Schwarz lemma as an estimate of the gradient for holomorphic curves, p. 217-231 in [AL]. | MR 1274931

[MW] M. Micallef, B. White, The structure of branch points in minimal surfaces and pseudoholomorphic curves, preprint 1994.

[Pa] P. Pansu, Compactness, p. 233-249 in [AL]. | MR 1274932

[Ra] P. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 31 (1978), 157-184. | Article | MR 467823 | Zbl 0358.70014

[Si] J.-C. Sikorav, Some properties of holomorphic curves in almost complex manifolds, p. 165-189 in [AL]. | MR 1274929

[SU] J. Sacks, K. Uhlenbeck, The existence of minimal immersions of two spheres, Ann. of Math. 113 (1981), 1-24. | Article | MR 604040 | Zbl 0462.58014

[Ve] I. N. Vekua, Generalized analytical functions, Pergamon, London, 1962. | MR 150320

[Vi] C. Viterbo, A proof of the Weinstein conjecture in 𝐑 2 n , Ann. Inst. Henri Poincaré, Analyse non linéaire 4 (1987), 337-357. | Article | Numdam | MR 917741 | Zbl 0631.58013

[We] A. Weinstein, On the hypotheses of Rabinowitz's periodic orbit theorems, J. Diff. Eq. 33 (1979), 353-358. | Article | MR 543704 | Zbl 0388.58020