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The General Definition of the Complex Monge–Ampère Operator on Compact Kähler Manifolds
Published online by Cambridge University Press: 20 November 2018
Abstract
We introduce a wide subclass $\mathcal{F}\left( X,\,\omega \right)$ 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 $\mathcal{F}\left( X,\,\omega \right)$ is a convex cone and includes all quasi-plurisubharmonic functions that are in the Cegrell class.
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- Copyright © Canadian Mathematical Society 2010
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