Surveys in Differential Geometry

Volume 17 (2012)

Complex Monge-Ampère equations

Pages: 327 – 410



D. H. Phong (Department of Mathematics, Columbia University)

Jian Song (Department of Mathematics, Rutgers University, Piscataway, N.J., U.S.A.)

Jacob Sturm (Department of Mathematics, Rutgers University, Newark, N.J., U.S.A.)


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.

Published 15 March 2013