Surveys in Differential Geometry
Volume 17 (2012)
Complex Monge-Ampère equations
Pages: 327 – 410
This is a survey of some of the recent developments in the theory of complex Monge-Ampère 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.