The General Definition of the Complex Monge-Ampère Operator on Compact Kähler Manifolds

Abstract

We introduce a wide subclass $\mathcal{F}(X,\omega )$ of quasi-plurisubharmonic functions in a compact Kähler manifold, on which the complex Monge-Ampère operator is well-defined and the convergence theorem is valid. We also prove that $\mathcal{F}(X,\omega )$ is a convex cone and includes all quasi-plurisubharmonic functions which are in the Cegrell class.

Cited by in corpus (1)

• Domains of definition of Monge-Ampère operators on compact Kähler manifolds