On boundary properties of asymptotically holomorphic functions

TL;DR

This paper establishes a Fatou type theorem for bounded functions with controlled growth of their d_J -bar differential on smoothly bounded domains within almost complex manifolds, extending classical boundary behavior results.

Contribution

It introduces a new boundary behavior theorem for asymptotically holomorphic functions in almost complex manifolds, generalizing classical complex analysis results.

Findings

Proves a Fatou type theorem for specific bounded functions.

Extends boundary behavior analysis to almost complex manifolds.

Provides conditions for controlled growth of the d_J -bar differential.

Abstract

We prove a Fatou type theorem for bounded functions with d_J -bar differential of a controled growth on smoothly bounded domains in an almost complex manifold.