Boundary Values and Boundary Uniqueness of $J$-Holomorphic Mapping

TL;DR

This paper extends classical boundary behavior theorems to $J$-holomorphic mappings, establishing boundary value properties, zero set conditions, and uniqueness results in the context of almost complex structures.

Contribution

It introduces boundary value theorems, zero set conditions, and uniqueness results specifically for $J$-holomorphic mappings, expanding classical complex analysis to almost complex manifolds.

Findings

Established a Fatou-type boundary theorem for $J$-holomorphic maps.

Proved the Blaschke condition for zero sets of these mappings.

Demonstrated a Privalov-type uniqueness theorem for pairs of $J$-holomorphic mappings.

Abstract

We establish a Fatou-type Theorem for $J$-holomorphic mappings that are bounded in an appropriate sense and we prove the Blaschke condition for their zero sets. We also prove a Privalov-type uniqueness Theorem for pairs of $J$-holomorphic mappings.