# The General Definition of the Complex Monge-Ampère Operator on Compact Kähler Manifolds - Mathematics > Complex Variables

Abstract: We introduce a wide subclass ${\cal F}(X,\omega)$ of quasi-plurisubharmonicfunctions in a compact K\-ahler manifold, on which the complex Monge-Amp\`ereoperator is well-defined and the convergence theorem is valid. We also provethat ${\cal F}(X,\omega)$ is a convex cone and includes allquasi-plurisubharmonic functions which are in the Cegrell class.

Author: Yang Xing

Source: https://arxiv.org/