Continuity of the complex Monge-Ampère operator

Xing, Yang

doi:10.1090/S0002-9939-96-03316-3

Continuity of the complex Monge-Ampère operator
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by Yang Xing

Proc. Amer. Math. Soc. 124 (1996), 457-467

DOI: https://doi.org/10.1090/S0002-9939-96-03316-3

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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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