Taming symplectic forms and the Calabi-Yau equation

Valentino Tosatti; Ben Weinkove; Shing Tung Yau

doi:10.1112/plms/pdn008

Taming symplectic forms and the Calabi-Yau equation

Valentino Tosatti^*, Ben Weinkove, Shing Tung Yau

^*Corresponding author for this work

Mathematics

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

62 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	401-424
Number of pages	24
Journal	Proceedings of the London Mathematical Society
Volume	97
Issue number	2
DOIs	https://doi.org/10.1112/plms/pdn008
State	Published - Sep 2008

Funding

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.

ASJC Scopus subject areas

General Mathematics

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10.1112/plms/pdn008

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abstract = "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.",

author = "Valentino Tosatti and Ben Weinkove and Yau, {Shing Tung}",

note = "Funding Information: 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.",

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N2 - 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.

AB - 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.

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Taming symplectic forms and the Calabi-Yau equation

Abstract

Funding

ASJC Scopus subject areas

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