The complex Monge-Ampère equation and pluripotential theory

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On stability and continuity of bounded solutions of degenerate complex Monge–Ampère equations over compact Kähler manifolds (2010, background): “One possible application of such a result would be a criterion for Hölder continuity of the Siciak Extremal Function of certain compact sets in C (see [13] for more discussion).”
A priori estimates for complex Hessian equations (2011, methodology): “By the inequality between mixed Monge–Ampère measures (see [Kołodziej 2005; Dinew 2009]) (ddcv)m∧ωn−m ≥ [V (K )](2 χKω.”
Bergman kernels and equilibrium measures for line bundles over projective manifolds (2007, methodology): “The proof of the C1,1-regularity of the equilibrium metric (on the complement of the augmented base locus of L) is partly modeled on the proof of Bedford-Taylor [2], [29] for C1,1-regularity of the solution of the Dirichlet problem (with smooth boundary data) for the complex Monge-Ampere equation in”