Symplectic analog of Calabi's conjecture for Calabi--Yau threefolds
  In this paper we state an analog of Calabi's conjecture proved by Yau. The difference with the classical case is that we propose deformation of the complex structure, whereas the complex Monge--Amp\`{e}re equation describes deformation of the K\"{a}hler (symplectic) structure. 
Dmitry V. Egorov
math.DG