The Calabi-Yau equation on the Kodaira-Thurston manifold

Abstract

We prove that the Calabi-Yau equation can be solved on the Kodaira-Thurston manifold for all given $T^2$-invariant volume forms. This provides support for Donaldson's conjecture that Yau's theorem has an extension to symplectic four-manifolds with compatible but non-integrable almost complex structures.

12 pages

References in corpus (1)

• Taming symplectic forms and the Calabi-Yau equation

Cited by in corpus (3)

• $C^{2,\alpha }$ estimates for nonlinear elliptic equations in complex and almost complex geometry
• A Cheng-Yau type estimate for the symplectic Calabi-Yau equation
• A note on tame/compatible almost complex structures on four-dimensional Lie algebras