arXiv:1104.0362 Abstract | arXiv Analytics

arXiv:1104.0362 [math.DG]Abstract References Reviews Resources

Complex solutions of Monge-Ampère equations

Published 2011-04-03, updated 2011-06-30Version 2

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.

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

DOI: 10.1016/j.geomphys.2011.06.019

Categories: math.DG, math-ph, math.AP, math.CV, math.MP

Keywords: monge-ampère equations, complex solutions, construct explicit holomorphic solutions, complex partial differential equations, reduce partial differential equations

Tags: journal article

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