Abstract
A C2 function on ℂn 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.
Original language | English (US) |
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Pages (from-to) | 311-346 |
Number of pages | 36 |
Journal | Journal of the American Mathematical Society |
Volume | 30 |
Issue number | 2 |
DOIs | |
State | Published - 2017 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics