A Cheng-Yau type estimate for the symplectic Calabi-Yau equation
Valentino Tosatti
TL;DR
This paper establishes a Cheng-Yau type a priori estimate for the symplectic Calabi-Yau equation, advancing understanding in symplectic geometry and potentially impacting solutions to Donaldson's conjecture.
Contribution
It introduces a novel a priori estimate for the symplectic Calabi-Yau equation, extending classical Cheng-Yau estimates to a symplectic setting.
Findings
Proves an a priori estimate for the symplectic Calabi-Yau equation.
Extends classical Cheng-Yau estimates to symplectic 4-manifolds.
Provides progress towards Donaldson's conjecture in symplectic geometry.
Abstract
In the setting of Donaldson's conjecture on the Calabi-Yau equation on symplectic 4-manifolds, we prove an a priori estimate which in the K\"ahler case resembles a classical estimate of Cheng-Yau.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Geometry and complex manifolds · Advanced Algebra and Geometry