Complex solutions of Monge-Amp\`ere equations
Differential Geometry
2015-05-27 v2 Mathematical Physics
Analysis of PDEs
Complex Variables
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.
Cite
@article{arxiv.1104.0362,
title = {Complex solutions of Monge-Amp\`ere equations},
author = {Bertrand Banos},
journal= {arXiv preprint arXiv:1104.0362},
year = {2015}
}
Comments
16 pages, 5 tables To appear in Journal of Geometry and Physics