Complex solutions of Monge-Ampère equations

Details Complex solutions of Monge-Ampère equations Complex solutions of Monge-Ampère equations

2011-04-03

arxiv.org/abs/1104.0362v2

Mathematics

Differential Geometry

16 pages, 5 tables To appear in Journal of Geometry and Physics

Scientific paper

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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