Abstract
Our aim in this paper is to characterize smooth domains (D, J) and (D , J ) in almost complex manifolds of real dimension 2n + 2 with a covering orbit {fk (p)}, accumulating at a strongly pseudoconvex boundary point, for some (J, J )-holomorphic coverings fk : (D, J). (D , J ) and p. D. It was shown that such domains are both biholomorphic to a model domain, if the source domain (D, J) admits a bounded strongly J plurisubharmonic exhaustion function. Furthermore, if the target domain (D , J ) is strongly pseudoconvex, then both (D, J) and (D , J ) are biholomorphic to the unit ball in Cn+ 1 with the standard complex structure. Our results can be considered as compactness theorems for sequences of pseudo-holomorphic coverings. Lin and Wong (Rocky Mt J Math 20(1): 179197, 1990) and Ourimi (Proc AMS 128(3): 831-836, 2000) generalize for relatively compact domains in almost complex manifolds.