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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Continuity of the complex Monge-Ampère operator
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by Yang Xing PDF
Proc. Amer. Math. Soc. 124 (1996), 457-467 Request permission


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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Additional Information
  • Yang Xing
  • Affiliation: Department of Mathematics, University of Umeå, S-901 87 Umeå, Sweden
  • Email:
  • Received by editor(s): August 15, 1994
  • Additional Notes: Partially supported by the Swedish Natural Science Research Council.
  • Communicated by: Eric Bedford
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 457-467
  • MSC (1991): Primary 32F07; Secondary 32F05
  • DOI:
  • MathSciNet review: 1322940