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Inventiones mathematicae

, Volume 82, Issue 2, pp 307–347 | Cite as

Pseudo holomorphic curves in symplectic manifolds

  • M. Gromov
Article

Keywords

Manifold Symplectic Manifold Holomorphic Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [Be] Bers, L.: An outline of the theory of pseudoanalytic functions. Bull. Am. Math. Soc.62, 291–332 (1956)Google Scholar
  2. [Ben] Bennequin, D.: Enlacements et équations de Pfaff. Astérisque107–108, 87–162 (1982)Google Scholar
  3. [Ber] Berger, M.: Du côté de chez Pu. Ann. Sci. Ec. Norm. Super., IV. Ser.4, 1–44 241–260 (1972)Google Scholar
  4. [B-G] Bedford, E., Gaveau, B.: Envelopes of holomorphy of certain 2-spheres in ℂ2. Am J. Math.105, 975–1009 (1983)Google Scholar
  5. [B-H] Begher, H., Hile, G.: Riemann boundary value problem for non-linear elliptic systems. In: Complex Variables, vol. 1, pp. 239–261. U.S.A.: Gordon and Breach 1983Google Scholar
  6. [Bi1] Bishop, E.: Conditions for the analyticity of certain sets. Mich. Math. J.11, 289–304 (1964)Google Scholar
  7. [Bi2] Bishop, E.: Differentiable manifolds in complex Euclidean space. Duke Math. J.32, 1–22 (1965)Google Scholar
  8. [B-Z] Burago, Yu., Zalgaller, V.: Geometric inequalities (in Russian). Leningrad, Nauka 1980 (an English translation is to appear in Springer-Verlag)Google Scholar
  9. [Ch] Chaperon, M.: Questions de géométrie symplectique. Sem. Sud-Rhodanien IV, Balarue, in Travaux en cours. Paris: Hermann 1984 (To appear)Google Scholar
  10. [C-Z] Conley, C., Zehnder, E.: The Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnold. Invent. math.73, 33–49 (1983)Google Scholar
  11. [D-D] Dazord, P., Desolneux-Moulis, N. (eds.): Séminaire Sud-Rhodanien de Géométrie. Paris: Hermann 1984Google Scholar
  12. [E-S] Eells, J., Salamon, S.: Twistorial constructions of harmonic maps of surfaces into fourmanifolds. Warwick, 1984 (Preprint)Google Scholar
  13. [El1] Eliashberg, Ya.: Estimates on the number of fixed points of area preserving transformations (in Russian) Syktyvkar, 1978 (Preprint)Google Scholar
  14. [El2] Eliashberg, Ya.: Rigidity of symplectic and contact structures (Preprint 1981)Google Scholar
  15. [F 1] Floer, A.: Proof of the Arnold conjecture for surfaces and generalizations for certain Kähler manifolds. Bochum (Preprint 1984)Google Scholar
  16. [F-W] Fortune, B., Weinstein, A.: A symplectic fixed point theorem for complex projective spaces. Berkeley (Preprint 1984)Google Scholar
  17. [Gil] Gilbert, R. (ed.): Proc. of the special session on elliptic systems in the plane. 87th Ann. Meeting of A.M.S. San Francisco, CA (1981)Google Scholar
  18. [G-W] Gluck, H., Warner, F.: Great circle fibrations of the three sphere. Duke Math. J.50, 107–132 (1983)Google Scholar
  19. [Gro1] Gromov, M.: A topological technique for the construction of solutions of differential equations and inequalities. ICM 1970, Nice,2, 221–225 (1971)Google Scholar
  20. [Gro2] Gromov, M.: Pseudo-holomorphic curves in symplectic manifolds, II. Berlin-Heidelberg-New York-Tokyo: Springer (In press)Google Scholar
  21. [Gro3] Gromov, M.: Partial differential relations. Berlin-Heidelberg-New York-Tokyo: Springer (In press)Google Scholar
  22. [H-L] Harvey, R., Lawson, B.: Calibrated geometries. Acta Math.148, 48–156 (1982)Google Scholar
  23. [H] Hofer, H.: Lagragian embedding and critical point theory. (Preprint 1984)Google Scholar
  24. [Lav] Lavrentiev, M.: A fundamental theorem of the theory of quasi-conformal mappings of plane regions. Izv. Akad. Nauk SSSR12, 513–554 (1948)Google Scholar
  25. [Law1] Lawson, B.: Lectures on minimal submanifolds (2e édition). Berkeley: Publish or Perish 1980Google Scholar
  26. [Law2] Lawson, B.: Surfaces minimales et la construction de Calabi-Penrose. Sém. Bourbaki no 625 (1983/84)Google Scholar
  27. [L-S] Laudenbach, F., Sikorav, J.C.: Persistance d'intersection avec la section nulle au cours d'une isotopie hamiltonienne dans un fibre cotangent. Invent. math.82, 349–357 (1985)Google Scholar
  28. [McD] McDuff, D.: (to appear)Google Scholar
  29. [Mo] Moser, J.: On the volume elements on a manifold. Trans. Am. Math. Soc.120, 286–294 (1965)Google Scholar
  30. [N-W] Nijehuis, A., Wolf, W.: Some integration problem in almost complex and complex manifolds. Ann. Math.77, 424–489 (1963)Google Scholar
  31. [Nir] Nirenberg, L.: Topics in non-linear functional analysis. Lect. Notes by R.A. Artino. Courant Inst. N.Y. Univ., N.Y. 1974Google Scholar
  32. [Ren] IIIe Rencontre de Géométrie du Schnepfenried. Astérisque107–108 (1982)Google Scholar
  33. [Sch] Schapiro, Z.: Sur l'existence des représentations quasiconformes. C.R. (Doklady) Acad. Sci. URSS3, 690–692 (1941)Google Scholar
  34. [St] Stoll, W.: The growth of the area of transcendental analytic set, I and II. Math. Ann.156, 47–98, 144–170 (1964)Google Scholar
  35. [Si] Sikorav, J.-C.: Points fixes d'une application symplectique homologue à l'identité. Orsay (Preprint 1984)Google Scholar
  36. [S-U] Sacks, J., Uhlenbeck, K.: The existence of minimal immersions of two-spheres. Ann. Math.113, 1–24 (1981)Google Scholar
  37. [Vek] Vekua, I.N.: Generalized analytic functions. London: Pergamon 1962Google Scholar
  38. [We] Wells, R.: Function theory on differential submanifolds. In: Contribution to Analysis, Ahlphors, L. (ed.), pp. 407–437. New York, London: Academic Press 1974Google Scholar
  39. [Wei] Weinstein, A.: Lectures on symplectic manifolds. A.M.S. Conf. Board, Reg. Conf. in Math.29 (1977)Google Scholar
  40. [Wen] Wendland, W.: Elliptic systems in the plane. London: Pitman 1978Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • M. Gromov
    • 1
  1. 1.Institut des Hautes Etudes ScientifiquesBures-sur-YvetteFrance

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