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

Hervé Gaussier, Alexandre Sukhov (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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.

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

Hervé Gaussier, Alexandre Sukhov (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

We consider a compact almost complex manifold ( M , J , ω ) with smooth Levi convex boundary M and a symplectic tame form ω . Suppose that S 2 is a real two-sphere, containing complex elliptic and hyperbolic points and generically embedded into M . We prove a result on filling S 2 by holomorphic discs.

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