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

59 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

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Mathematics(all)

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10.1112/plms/pdn008

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title = "Taming symplectic forms and the Calabi-Yau equation",

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.",

year = "2008",

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AU - Weinkove, Ben

AU - Yau, Shing Tung

N1 - 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.

PY - 2008/9

Y1 - 2008/9

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

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