The Calabi-Yau Equation on Symplectic Manifolds
Differential Geometry
2023-11-30 v1 Symplectic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.2311.17610,
title = {The Calabi-Yau Equation on Symplectic Manifolds},
author = {Qiang Tan and Hongyu Wang},
journal= {arXiv preprint arXiv:2311.17610},
year = {2023}
}