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

Published:2009-12-04
Printed: Feb 2010
• Yang Xing,
Lund University, Sweden
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## 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 that are in the Cegrell class.
 Keywords: complex Monge--Ampère operator, compact Kähler manifold
 MSC Classifications: 32W20 - Complex Monge-Ampere operators 32Q15 - Kahler manifolds