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

Tosatti, Valentino¹ ; Weinkove, Ben¹

¹ Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208

Journal of the American Mathematical Society, Tome 30 (2017) no. 2, pp. 311-346

Résumé

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.

Détail

DOI : 10.1090/jams/875

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