Complex Monge Ampere Equations

TL;DR

This survey reviews recent advances in the theory of complex Monge-Ampere equations, covering estimates, pluripotential methods, variational approaches, and solution constructions.

Contribution

It compiles and discusses recent developments and techniques in complex Monge-Ampere equations, highlighting new methods and theoretical insights.

Findings

Refinements of classical a priori estimates

Application of pluripotential theory methods

Variational methods for big cohomology classes

Abstract

This is a survey of some of the recent developments in the theory of complex Monge-Ampere equations. The topics discussed include refinements and simplifications of classical a priori estimates, methods from pluripotential theory, variational methods for big cohomology classes, semiclassical constructions of solutions of homogeneous equations, and envelopes.