Geometric pluripotential theory on Kähler manifolds

Source 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.