The Monge-Amp\`ere equation for non-integrable almost complex structures

TL;DR

This paper proves the existence and uniqueness of solutions to the Monge-Ampère equation on compact almost complex manifolds with non-integrable structures, extending classical results to a broader geometric setting.

Contribution

It introduces a framework for solving the Monge-Ampère equation in the context of non-integrable almost complex structures, which was previously unexplored.

Findings

Existence of solutions established

Uniqueness of solutions proven

Extension of Monge-Ampère theory to non-integrable structures

Abstract

We show existence and uniqueness of solutions to the Monge-Ampere equation on compact almost complex manifolds with non-integrable almost complex structure.