The non-linear Cousin problem for $J$-holomorphic maps

TL;DR

This paper introduces a method to solve the non-linear Cousin problem for J-holomorphic maps, enabling the gluing of pseudoholomorphic maps on complex domains, advancing the understanding of their structure.

Contribution

It provides a novel gluing technique for pseudoholomorphic maps on Cartan pairs, addressing a non-linear Cousin problem in complex analysis.

Findings

Established a gluing method for J-holomorphic maps

Solved the non-linear Cousin problem in this context

Enhanced the toolkit for studying pseudoholomorphic maps

Abstract

We solve the non-linear Cousin problem for $J$-holomorphic maps. That is, we provide a gluing method for the pseudoholomorphic maps defined on a Cartan pair of domains in $\mathbb{C}$.