# Optimal transport on completely integrable toric manifolds

## TL;DR

This paper demonstrates that solutions to the transported Monge-Ampere problem on complex compact toric manifolds can be established using the real optimal transportation theory, simplifying previous approaches.

## Contribution

It bridges complex Monge-Ampere equations on toric manifolds with real optimal transportation theory, providing a new, streamlined proof of existence and uniqueness.

## Key findings

- Existence and uniqueness of solutions established
- Connections between complex and real optimal transport theories
- Simplified proof approach for Monge-Ampere problems

## Abstract

We show that existence and uniqueness of solutions to transported Monge-Ampere problem on complex compact toric manifold follows easily from the real theory of optimal transportation.