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

Valentino Tosatti, Ben Weinkove

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)311-346
Number of pages36
JournalJournal of the American Mathematical Society
Volume30
Issue number2
DOIs
StatePublished - 2017

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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