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

Part of: Differential operators in several variables Complex manifolds

Published online by Cambridge University Press:  20 November 2018

Yang Xing
Yang Xing*
Affiliation:
Centre for Mathematical Sciences, Lund University, SE-22100, Lund, Sweden, e-mail: yang.xing@math.lth.se
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Abstract

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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.

Keywords

complex Monge-Ampère operatorcompact Kähler manifold

MSC classification

Secondary: 32W20: Complex Monge-Ampère operators 32Q15: Kähler manifolds
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 1 , 01 February 2010 , pp. 218 - 239
Copyright
Copyright © Canadian Mathematical Society 2010

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