Levi-flat filling of real two-spheres in symplectic manifolds (I)

Gaussier, Hervé; Sukhov, Alexandre

doi:10.5802/afst.1316

Gaussier, Hervé ; Sukhov, Alexandre

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 20 (2011) no. 3, pp. 515-539.

Résumé
Abstract

Soit $(M, J, ω)$ une variété dont la structure presque complexe $J$ est contrôlée par la forme symplectique $ω$ . On suppose $M$ de dimension complexe deux, Levi-convexe et à géométrie bornée. On démontre que toute 2-sphère possédant deux points elliptiques et plongée dans le bord de $M$ est feuilletée par des bords de disques pseudoholomorphes.

Let $(M, J, ω)$ be a manifold with an almost complex structure $J$ tamed by a symplectic form $ω$ . We suppose that $M$ has the complex dimension two, is Levi-convex and with bounded geometry. We prove that a real two-sphere with two elliptic points, embedded into the boundary of $M$ can be foliated by the boundaries of pseudoholomorphic discs.

MR 2894837 | Zbl 1242.53107 | 2 citations dans Numdam

DOI : https://doi.org/10.5802/afst.1316

@article{AFST_2011_6_20_3_515_0,
     author = {Gaussier, Herv\'e and Sukhov, Alexandre},
     title = {Levi-flat filling of real two-spheres in symplectic manifolds (I)},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {515--539},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 20},
     number = {3},
     year = {2011},
     doi = {10.5802/afst.1316},
     mrnumber = {2894837},
     zbl = {1242.53107},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/afst.1316/}
}

Gaussier, Hervé; Sukhov, Alexandre. Levi-flat filling of real two-spheres in symplectic manifolds (I). Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 20 (2011) no. 3, pp. 515-539. doi : 10.5802/afst.1316. http://www.numdam.org/articles/10.5802/afst.1316/

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