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

Open Access article
 Printed: Feb 2010
  • Yang Xing,
    Lund University, Sweden
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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 complex Monge--Ampère operator, compact Kähler manifold
MSC Classifications: 32W20, 32Q15 show english descriptions Complex Monge-Ampere operators
Kahler manifolds
32W20 - Complex Monge-Ampere operators
32Q15 - Kahler manifolds

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