Extension and convergence theorems of pseudoholomorphic maps

Abstract

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.