Gromov hyperbolicity of strongly pseudoconvex almost complex manifolds

Abstract

Let D = {ρ & 0} be a smooth relatively compact domain in an almost complex manifold (M,J), where ρ is a smooth defining function of D, strictly J-plurisubharmonic in a neighborhood of the closure D of D. We prove that D has a connected boundary and is Gromov hyperbolic. © 2015, American Mathematical Society.