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Continuity of the complex Monge-Ampère operator

Author: Yang Xing
Journal: Proc. Amer. Math. Soc. 124 (1996), 457-467
MSC (1991): Primary 32F07; Secondary 32F05
MathSciNet review: 1322940
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Abstract: The complex Monge-Ampère operator $(dd^c)^n$ is an important tool in complex analysis. It would be interesting to find the right notion of convergence $u_j\to u$ such that $(dd^cu_j)^n\to (dd^cu)^n$ in the weak topology. In this paper, using the $C_{n-1}$-capacity, we give a sufficient condition of the weak convergence $(dd^cu_j)^n\to (dd^cu)^n$. We also show that our condition is quite sharp in some case.

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Yang Xing
Affiliation: Department of Mathematics, University of Umeå, S-901 87 Umeå, Sweden

Keywords: Plurisubharmonic function, complex Monge-Ampère operator
Received by editor(s): August 15, 1994
Additional Notes: Partially supported by the Swedish Natural Science Research Council.
Communicated by: Eric Bedford
Article copyright: © Copyright 1996 American Mathematical Society