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Let be a manifold with an almost complex structure tamed by a symplectic form . We suppose that 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 can be foliated by the boundaries of pseudoholomorphic discs.
We consider a compact almost complex manifold with smooth Levi convex boundary and a symplectic tame form . Suppose that is a real two-sphere, containing complex elliptic and hyperbolic points and generically embedded into . We prove a result on filling by holomorphic discs.
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