Asymptotic behaviour of holomorphic strips

Joel W Robbin; Dietmar A Salamon

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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.