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arXiv · 1305.7511

The Monge-Amp\`ere equation for (n-1)-plurisubharmonic functions on a compact K\"ahler manifold

Valentino Tosatti·Ben Weinkove
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Abstract

A C^2 function on 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 nonnegative. We show that the associated Monge-Ampere equation can be solved on any compact Kahler 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 Kahler manifolds.

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Valentino Tosatti, Ben Weinkove. 2013-05-31. The Monge-Amp\`ere equation for (n-1)-plurisubharmonic functions on a compact K\"ahler manifold. https://doi.org/10.1090/jams%2F875

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