Taming symplectic forms and the Calabi-Yau equation

2007/03/26 by Valentino Tosatti, Ben Weinkove, Shing-Tung Yau · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Citation #Computer science #Geometry and complex manifolds #History #Library science #Mathematics #Sociology #Subject (documents) #math.DG #math.SG

paper · pdf · doi:10.1112/plms/pdn008

published as Proc. London Math. Soc. 97 (2008), no.2, 401-424. · 32 pages

arxiv created 2007/03/26 · openalex publication_date 2008/03/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• The Space of Kähler metrics (II)
• Multiplier Ideal Sheaves and the Kähler-Ricci Flow
• Improper affine hyperspheres of convex type and a generalization of a theorem by K. Jörgens.
• On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I
• Introduction to Complex Analysis in Several Variables
• Characteristic Classes of Hermitian Manifolds

Cited by

• Adiabatic limits of Ricci-flat Kähler metrics