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arXiv · 1607.02621

The Aleksandrov-Bakelman-Pucci estimate and the Calabi-Yau equation

Valentino Tosatti·Ben Weinkove
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Abstract

We give two applications of the Aleksandrov-Bakelman-Pucci estimate to the Calabi-Yau equation on symplectic four-manifolds. The first is solvability of the equation on the Kodaira-Thurston manifold for certain almost-Kahler structures assuming $S^1$-invariance, extending a result of Buzano-Fino-Vezzoni. The second is to reduce the general case of Donaldson's conjecture to a bound on the measure of a superlevel set of a scalar function.

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BibTeXRIS

Valentino Tosatti, Ben Weinkove. 2016-07-09. The Aleksandrov-Bakelman-Pucci estimate and the Calabi-Yau equation. https://arxiv.org/abs/1607.02621

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