Following the work of Berman and Witt Nyström we present the proof of existence and uniqueness of solutions to transported Monge–Ampère problem on complex compact manifolds with completely integrable torus action. The proof is based on the real theory of optimal transportation and some convex analysis.

中文翻译：

---

完全可积分的Toric流形上的最佳运输

继Berman和WittNyström的工作之后，我们提出了在具有完全可积分的环面作用的复杂紧凑流形上运输Monge-Ampère问题的解的存在性和唯一性的证明。该证明基于最佳运输的真实理论和一些凸分析。