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# Surveys in Differential Geometry

## Volume 17 (2012)

### Complex Monge-Ampère equations

Pages: 327 – 410

DOI: http://dx.doi.org/10.4310/SDG.2012.v17.n1.a8

#### Authors

#### Abstract

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.