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Complex solutions of Monge-Ampère equations (1104.0362v2)
Published 3 Apr 2011 in math.DG, math-ph, math.AP, math.CV, and math.MP
Abstract: We describe a method to reduce partial differential equations of Monge-Amp`ere type in 4 variables to complex partial differential equations in 2 variables. To illustrate this method, we construct explicit holomorphic solutions of the special lagrangian equation, the real Monge-Amp`ere equations and the Plebanski equations.
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