Orbites périodiques et courbes pseudo-holomorphes. Application à la conjecture de Weinstein en dimension 3
Séminaire Bourbaki (1993-1994)
- Volume: 36, page 309-333
- ISSN: 0303-1179
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topLaudenbach, François. "Orbites périodiques et courbes pseudo-holomorphes. Application à la conjecture de Weinstein en dimension 3." Séminaire Bourbaki 36 (1993-1994): 309-333. <http://eudml.org/doc/110189>.
@article{Laudenbach1993-1994,
author = {Laudenbach, François},
journal = {Séminaire Bourbaki},
keywords = {contact manifold; symplectic manifold; characteristic foliation; compact foliations; periodic orbits; pseudo-holomorphic curves},
language = {fre},
pages = {309-333},
publisher = {Société Mathématique de France},
title = {Orbites périodiques et courbes pseudo-holomorphes. Application à la conjecture de Weinstein en dimension 3},
url = {http://eudml.org/doc/110189},
volume = {36},
year = {1993-1994},
}
TY - JOUR
AU - Laudenbach, François
TI - Orbites périodiques et courbes pseudo-holomorphes. Application à la conjecture de Weinstein en dimension 3
JO - Séminaire Bourbaki
PY - 1993-1994
PB - Société Mathématique de France
VL - 36
SP - 309
EP - 333
LA - fre
KW - contact manifold; symplectic manifold; characteristic foliation; compact foliations; periodic orbits; pseudo-holomorphic curves
UR - http://eudml.org/doc/110189
ER -
References
top- [AL] M. Audin, J. Lafontaine, eds., Holomorphic curves in symplectic geometry, Birkhäuser, 1994. Zbl0802.53001MR1274923
- [Be1] D. Bennequin, Entrelacements et équations de Pfaff, Astérisque103- 108 (1983), 83-161. Zbl0573.58022MR753131
- [Be2] D. Bennequin, Caustique mystique [d'après Arnold et al.], Sém. Bourbaki, Astérisque133-134 (1986), 19-56. Zbl0632.58011MR837213
- [Be3] D. Bennequin, Problèmes elliptiques, surfaces de Riemann et structures symplectiques [d'après M. Gromov], Sém. Bourbaki, Astérisque145- 146 (1987), 111-136. Zbl0644.53031MR880029
- [BG] E. Bedford, B. Gaveau, Envelopes of holomorphy of certain 2-spheres in C2, Amer. J. of Math.105 (1983), 975-1009. Zbl0535.32008MR708370
- [Ber] H. Berestycki, Solutions périodiques de systèmes hamiltoniens, Sém. Bourbaki, Astérisque105-106 (1983), 105-128. Zbl0526.58016MR728984
- [Bers] L. Bers, An outline of the theory of pseudo-analytic functions, Bull. Amer. Math. Soc.62 (1956), 291-331. Zbl0072.07703MR81936
- [Bi] E. Bishop, Differentiable manifolds in complex Euclidian space, Duke Math. J. Zbl0154.08501MR200476
- [El1] Y. Eliashberg, Classification of overtwisted contact structures on 3- manifolds, Invent. Math.98 (1989), 623-637. Zbl0684.57012MR1022310
- [El2] Y. Eliashberg, Filling by holomorphic discs and its applications, London Math. Soc. Lect. Notes Ser.151 (1991), 45-67. Zbl0731.53036MR1171908
- [El3] Y. Eliashberg, Contact 3-manifolds, twenty years since J. Martinet's work, Ann. Inst. Fourier42 (1992), 165-192. Zbl0756.53017MR1162559
- [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. Zbl0766.53028MR1129802
- [Gi2] E. Giroux, Topologie de contact en dimension trois [autour de travaux de Yakov Eliashberg], Sém. Bourbaki, Astérisque216 (1993), 7-34. Zbl0793.53037MR1246390
- [Gr] M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. math.82 (1985), 307-347. Zbl0592.53025MR1554036
- [Hed] G. Hedlund, Fuchsian groups and transitive horocycles, Duke Math. Journal2 (1936), 530-542. Zbl0015.10201MR1545946JFM62.0392.03
- [Hem] J. Hempel, 3-manifolds, Annals of Math. Studies, Princeton Univ. Press, 1976. Zbl0345.57001MR415619
- [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. Zbl0759.58016
- [Ho] H. Hofer, Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three, Invent. Math.114 (1993), 515-563. Zbl0797.58023MR1244912
- [HV] H. Hofer, C. Viterbo, The Weinstein conjecture in the presence of holomorphic spheres, Comm. Pure Appl. Math.45 (1992), 583-622. Zbl0773.58021MR1162367
- [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 SSSR81 (1951), 17-18. Zbl0045.20903MR44760
- [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. Zbl0215.23003MR350771
- [Mc1] D. McDuff, The structure of rational and ruled symplectic 4-manifolds, J. of AMS3 (1990), 672-712. Zbl0723.53019MR1049697
- [Mc2] D. McDuff, The local behaviour of holomorphic curves in almost complex 4-manifolds, J. of Diff. Geo.34 (1991), 143-164. Zbl0736.53038MR1114456
- [Mc3] D. McDuff, Symplectic manifolds with contact type boundaries, Invent. math.103 (1991), 651-671. Zbl0719.53015MR1091622
- [Mc4] D. McDuff, Singularities and positivity of intersections of J-holomorphic curves, p. 191-215 in [AL]. MR1274930
- [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. Studies84, Princeton Univ. Press, 1975. Zbl0305.57003MR418127
- [Mu] M.-P. Muller, Gromov's Schwarz lemma as an estimate of the gradient for holomorphic curves, p. 217-231 in [AL]. MR1274931
- [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]. MR1274932
- [Ra] P. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math.31 (1978), 157-184. Zbl0358.70014MR467823
- [Si] J.-C. Sikorav, Some properties of holomorphic curves in almost complex manifolds, p. 165-189 in [AL]. MR1274929
- [SU] J. Sacks, K. Uhlenbeck, The existence of minimal immersions of two spheres, Ann. of Math.113 (1981), 1-24. Zbl0462.58014MR604040
- [Ve] I.N. Vekua, Generalized analytical functions, Pergamon, London, 1962. MR150320
- [Vi] C. Viterbo, A proof of the Weinstein conjecture in R2n, Ann. Inst. Henri Poincaré, Analyse non linéaire 4 (1987), 337-357. Zbl0631.58013MR917741
- [We] A. Weinstein, On the hypotheses of Rabinowitz's periodic orbit theorems, J. Diff. Eq.33 (1979), 353-358. Zbl0388.58020MR543704
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