The Monge-Ampère equation for (𝑛-1)-plurisubharmonic functions on a compact Kähler manifold

Tosatti, Valentino; Weinkove, Ben

doi:10.1090/jams/875

The Monge-Ampère equation for $(n-1)$-plurisubharmonic functions on a compact Kähler manifold
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by Valentino Tosatti and Ben Weinkove

J. Amer. Math. Soc. 30 (2017), 311-346

DOI: https://doi.org/10.1090/jams/875

Published electronically: December 14, 2016

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Abstract:

A $C^2$ function on $\mathbb {C}^n$ is called $(n-1)$-plurisubharmonic in the sense of Harvey-Lawson if the sum of any $n-1$ eigenvalues of its complex Hessian is non-negative. We show that the associated Monge-Ampère equation can be solved on any compact Kähler manifold. As a consequence we prove the existence of solutions to an equation of Fu-Wang-Wu, giving Calabi-Yau theorems for balanced, Gauduchon, and strongly Gauduchon metrics on compact Kähler manifolds.

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