On holomorphic mappings between almost Hermitian manifolds

TL;DR

This paper extends Liouville-type results to almost complex manifolds by adapting techniques from complex geometry, addressing challenges posed by non-integrability, and providing a detailed proof of the main theorem.

Contribution

It introduces a novel approach to Liouville theorems in the non-integrable almost complex setting, building on and combining existing techniques.

Findings

Established a Liouville-type theorem for almost complex manifolds.

Identified key differences between integrable and non-integrable cases.

Developed new tools to handle non-integrability in complex geometry.

Abstract

Our goal is to combine the techniques of Xiaokui Yang, Valentino Tosatti, and others to establish a Liouville-type result for almost complex manifolds. The transition to the non-integrable setting is delicate, so we will devote a section to discuss the key differences, and another to introduce the tools we will be using. Afterwards, we present a proof of our main theorem.