Levi-flat filling of real two-spheres in symplectic manifolds (I)
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 20 (2011) no. 3, pp. 515-539.

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.

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.

DOI: 10.5802/afst.1316
Gaussier, Hervé 1; Sukhov, Alexandre 2

1 Université Joseph Fourier, 100 rue des Maths, 38402 Saint Martin d’Hères, France
2 Université des Sciences et Technologies de Lille, Laboratoire Paul Painlevé, U.F.R. de Mathématique, 59655 Villeneuve d’Ascq, Cedex, France
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Gaussier, Hervé; Sukhov, Alexandre. Levi-flat filling of real two-spheres in symplectic manifolds (I). Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 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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