English

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.

Keywords

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

R2 v1 2026-06-21T17:48:40.907Z