Geometric pluripotential theory on Kähler manifolds

Abstract

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.

arXiv commentv2. improved presentation