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Mathematics  2009 

The Calabi-Yau equation on the Kodaira-Thurston manifold

DOI: 10.1017/S1474748010000289

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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.

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