Taming symplectic forms and the Calabi-Yau equation

Valentino Tosatti*, Ben Weinkove, Shing Tung Yau

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)401-424
Number of pages24
JournalProceedings of the London Mathematical Society
Volume97
Issue number2
DOIs
StatePublished - 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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