2023/11/29 by Tan, Qiang, Wang, Hongyu
#Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2311.17610
By using the global deformation of almost complex structures which are compatible with a symplectic form off a Lebesgue measure zero subset, we construct a (measurable) Lipschitz Kahler metric such that the one-form type Calabi-Yau equation on an open dense submanifold is reduced to the complex Monge-Ampere equation with respect to the measurable Kahler metric. We give an existence theorem for solutions to the one-form type Calabi-Yau equation on closed symplectic manifolds.