Continuity of the complex Monge-Ampere operator

Yang Xing

Continuity of the complex Monge-Ampere operator

复变函数 2008-02-03 v1

作者: Yang Xing

摘要

The complex Monge-Amp\`ere 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.

引用

@article{arxiv.math/9406201,
  title  = {Continuity of the complex Monge-Ampere operator},
  author = {Yang Xing},
  journal= {arXiv preprint arXiv:math/9406201},
  year   = {2008}
}

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