The Calabi-Yau equation on the Kodaira-Thurston manifold

Valentino Tosatti; Ben Weinkove

doi:10.1017/S1474748010000289

The Calabi-Yau equation on the Kodaira-Thurston manifold

Valentino Tosatti, Ben Weinkove

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that the Calabi-Yau equation can be solved on the Kodaira-Thurston manifold for all given T²-invariant volume forms. This provides support for Donaldson's conjecture that Yau's theorem has an extension to symplectic 4-manifolds with compatible but non-integrable almost complex structures.

Original language	English (US)
Pages (from-to)	437-447
Number of pages	11
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	10
Issue number	2
DOIs	https://doi.org/10.1017/S1474748010000289
State	Published - Apr 2011

Keywords

Calabi-Yau
Kodaira-Thurston manifold
almost complex
symplectic

ASJC Scopus subject areas

General Mathematics

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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 T2-invariant volume forms. This provides support for Donaldson's conjecture that Yau's theorem has an extension to symplectic 4-manifolds with compatible but non-integrable almost complex structures.",

keywords = "Calabi-Yau, Kodaira-Thurston manifold, almost complex, symplectic",

author = "Valentino Tosatti and Ben Weinkove",

note = "Funding Information: Acknowledgements. This research was supported in part by National Science Foundation Grant DMS-08-48193. B.W. is also supported in part by a Sloan Foundation fellowship.",

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AB - We prove that the Calabi-Yau equation can be solved on the Kodaira-Thurston manifold for all given T2-invariant volume forms. This provides support for Donaldson's conjecture that Yau's theorem has an extension to symplectic 4-manifolds with compatible but non-integrable almost complex structures.

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The Calabi-Yau equation on the Kodaira-Thurston manifold

Abstract

Keywords

ASJC Scopus subject areas

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