Gluing complex discs to Lagrangian manifolds by Gromov’s method
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 22 (2013) no. 4, pp. 811-842.

L’article discute certains aspects de la théorie d’attachement des disques complexes aux variétés Lagrangiennes par la méthode de Gromov.

The paper discusses some aspects of Gromov’s theory of gluing complex discs to Lagrangian manifolds.

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     title = {Gluing complex discs to {Lagrangian} manifolds by {Gromov{\textquoteright}s} method},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {811--842},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 22},
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Sukhov, Alexandre; Tumanov, Alexander. Gluing complex discs to Lagrangian manifolds by Gromov’s method. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 22 (2013) no. 4, pp. 811-842. doi : 10.5802/afst.1389. http://www.numdam.org/articles/10.5802/afst.1389/

[1] Alexander (H.).— Gromov’s method and Bennequin’s problem, Invent. Math. 125, p. 135-148, (1996). | MR | Zbl

[2] Arnold (V.I.).— Symplectic geometry and topology, J. Math. Phys. 41, p. 3307-3343, (2000). | MR | Zbl

[3] Audin (M.), Lafontaine (J.) (Eds.).— “Holomorphic curves in symplectic geometry", Birkhauser, Progress in Mathematics, V.117 (1994). | MR | Zbl

[4] Bers (L.), Schechter (M.).— “Elliptic equations", 1964 Partial differential equations, p. 131-299, Interscience, New York, (1964). | MR | Zbl

[5] Chirka (E.M.).— “Complex analytic sets", Kluwer, (1989). | MR | Zbl

[6] Diederich (K.), Sukhov (A.).— Plurisubharmonic exhaustion functions and almost complex Stein structures, Mich. Math. J. 56, p. 331-355, (2008). | MR | Zbl

[7] Donaldson (S.).— What is ... a pseudoholomorphic curve?, Notices of the AMS, 52, p. 1026-1027, (2005). | MR | Zbl

[8] Duval (J.) and Gayet (D.).— Riemann surfaces and totally real tori, arXiv 0910.2139.

[9] Eliashberg (Y.), Traynor (L.) (Eds.).— “Symplectic geometry and topology", AMS, Princeton, NJ. (1997). | MR

[10] Gaussier (H.), Sukhov (A.).— Levi-flat filling of real two-spheres in symplectic manifolds (I),(II), Ann. Fac. Sci. Toulouse Math. , XX(2011), p. 515-539, XXI, p. 783-816, (2012). | Numdam | MR | Zbl

[11] Ivashkovich (S.), Shevchishin (V.).— “Complex curves in almost-complex manifolds and meromorphic hulls", Institut fur Math. Ruhr-Universitat Bochum, (1999).

[12] Ivashkovich (S.), Shevchishin (V.).— Reflection principle and J-complex curves with boundary on totally real immersions, Commun. Contem. Math. 4, p. 65–106, (2002). | MR | Zbl

[13] Gromov (M.).— Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 82, p. 307-347, (1985). | Zbl

[14] Hofer (H.), Lizan (V.), Sikorav (J.-C.).— On genericity for holomorphic curves in four-dimensional almost-complex manifolds, J.Geom. Anal. 7, p. 144-159, (1997). | MR | Zbl

[15] Hummel (Ch.).— “Gromov’s compactness theorem for pseudoholomorphic curves", Birkhauser, Progress in Mathematics V.151 (1997). | MR | Zbl

[16] McDuff (D.), Salomon (D.).— “Introduction to symplectic topology", 2nd edition, Ofxord University Press, (1998). | MR | Zbl

[17] McDuff (D.), Salomon (D.).— “J-holomorphic curves and symplectic topology", AMS, Coll. Publ. Vol. 52, (2004). | Zbl

[18] Mikallef (M.J.), White (B.).— The structure of branch points in minimal surfaces and in pseudoholomorphic curves, Ann. Math. 139, p. 35-85, (1994). | MR | Zbl

[19] Mikhlin (S.), Prössdorf (S.).— “Singular integral equations", Springer Verlag, Berlin, (1986).

[20] Morrey (Ch.B.), Jr.— “Multiple integrals in the calculus of variations", Springer Verlag. N.Y. (1966). | MR | Zbl

[21] Smale (S.).— An infinite dimensinal version of Sard’s theorem, Amer. J. Math. 87, p. 861-866, (1965). | MR | Zbl

[22] Sukhov (A.), Tumanov (A.).— Regularization of almost complex structures, Ann. Sc. Norm. Sup. Pisa. 10, p. 389-411, (2011). | Numdam | MR | Zbl

[23] Sukhov (A.), Tumanov (A.).— Deformation and transversality of pseudo-holomorphic discs , J. Anal. Math. 116, p. 1-16, (2012). | MR | Zbl

[24] Sukhov (A.), Tumanov (A.).— Boundary value problems and J-complex curves, arXiv 1103.0324, to appear in Complex Variables and Elliptic Equations (Special Issue).

[25] Vekua (I. N.).— “Generalized analytic functions", Pergamon Press, (1962). | MR | Zbl

[26] Wendland (W.L.).— “Elliptic systems in the plane", Pitman, (1979). | MR | Zbl

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