Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-96-03316-3
MathSciNet review: 1322940
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 32F07, 32F05

Retrieve articles in all journals with MSC (1991): 32F07, 32F05


Additional Information

Yang Xing
Affiliation: Department of Mathematics, University of Umeå, S-901 87 Umeå, Sweden
Email: yang.xing@mathdept.umu.se

DOI: https://doi.org/10.1090/S0002-9939-96-03316-3
Keywords: Plurisubharmonic function, complex Monge-Amp\`{e}re 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