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

Yang Xing

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arXiv · 0705.2099

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

Yang Xing

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Abstract

We introduce a wide subclass ${\cal F}(X,ω)$ 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 ${\cal F}(X,ω)$ is a convex cone and includes all quasi-plurisubharmonic functions which are in the Cegrell class.

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Yang Xing. 2007-05-15. The General Definition of the Complex Monge-Ampère Operator on Compact Kähler Manifolds. https://arxiv.org/abs/0705.2099

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