A note on the geometry of pseudoconvex domains of finite type in almost complex manifolds

Abstract

Let $D=\{\rho<0\}$ be a smooth domain of finite type in an almost complex manifold (M,J) of real dimension four. We assume that the defining function $\rho$ is J-plurisubharmonic on a neighborhood of $\overline{D}$. We study the asymptotic behavior of pseudoholomorphic discs contained in the domain D.