First, we generalize the big Picard theorem for pseudoholomorphic maps. Next, we prove Noguchi-type extension-convergence theorems for pseudoholomorphic maps. Finally, we show that the $J$-automorphism group of an almost complex submanifold hyperbolically embedded in a compact, almost complex manifold of real dimension 4 is finite when it is the complement of an immersed pseudoholomorphic curve.
"Extension and convergence theorems of pseudoholomorphic maps." Osaka J. Math. 46 (3) 821 - 844, September 2009.