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.

Soit $\left(M,J,\omega \right)$ une variété dont la structure presque complexe $J$ est contrôlée par la forme symplectique $\omega$. 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 $\left(M,J,\omega \right)$ be a manifold with an almost complex structure $J$ tamed by a symplectic form $\omega$. 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.

@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},
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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