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Proceedings of the London Mathematical Society Advance Access published online on March 28, 2008
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdn008
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© 2008 London Mathematical Society

Taming symplectic forms and the Calabi–Yau equation

Valentino Tosatti, Ben Weinkove and Shing-Tung Yau

Mathematics Department
Harvard University
1 Oxford Street
Cambridge, MA 02138
USA
weinkove@math.harvard.edu
yau@math.harvard.edu

Received 30 April 2007. Revision received 13 December 2007.

We study the Calabi–Yau equation on symplectic manifolds. We show that Donaldson's conjecture on estimates for this equation in terms of a taming symplectic form can be reduced to an integral estimate of a scalar potential function. Under a positive curvature condition, we show that the conjecture holds.

The first author is supported in part by a Jean de Valpine Fellowship, the second author is supported in part by NSF grant DMS 0504285 and the third author is supported in part by NSF grant DMS 0306600.

2000 Mathematics Subject Classification 53C99 (primary), 53D05, 32Q60 (secondary).


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