Kähler流形上的几何多重位势理论
Geometric pluripotential theory on Kähler manifolds
AI总结：
本综述从基本原理出发，介绍了Kähler几何中复Monge-Ampère型方程的有限能量多重位势理论，指出位势空间的度量几何可将变分问题转化为无限维凸优化问题，从而证明方程解的存在性。
摘要：
有限能量多重位势理论容纳了Kähler几何中产生的复Monge-Ampère型方程的变分理论。最近发现，所涉及的许多位势空间具有丰富的度量几何，有效地将所讨论的变分问题转化为无限维凸优化问题，从而为底层复Monge-Ampère方程的解提供了存在性结果。本综述旨在从基本原理出发描述这些进展。
英文摘要：
Finite energy pluripotential theory accommodates the variational theory of equations of complex Monge-Ampère type arising in Kähler geometry. Recently it has been discovered that many of the potential spaces involved have a rich metric geometry, effectively turning the variational problems in question into problems of infinite dimensional convex optimization, yielding existence results for solutions of the underlying complex Monge-Ampère equations. The purpose of this survey is to describe these developments from basic principles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
