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arXiv · 2311.17610

The Calabi-Yau Equation on Symplectic Manifolds

Qiang Tan·Hongyu Wang
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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.

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Qiang Tan, Hongyu Wang. 2023-11-29. The Calabi-Yau Equation on Symplectic Manifolds. https://arxiv.org/abs/2311.17610

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