Banach analytic sets and a non-linear version of the Levi extension theorem

Sergey Ivashkovich UFR de Mathématiques, Université de Lille-1

Complex Variables and Complex Analysis mathscidoc:1701.08011

Arkiv for Matematik, 52, (1), 149-173, 2012.4
We prove a certain non-linear version of the Levi extension theorem for meromorphic functions. This means that the meromorphic function in question is supposed to be extendable along a sequence of complex curves, which are arbitrary, not necessarily straight lines. Moreover, these curves are not supposed to belong to any finite-dimensional analytic family. The conclusion of our theorem is that nevertheless the function in question meromorphically extends along an (infinite-dimensional) analytic family of complex curves and its domain of existence is a pinched domain filled in by this analytic family.
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@inproceedings{sergey2012banach,
  title={Banach analytic sets and a non-linear version of the Levi extension theorem},
  author={Sergey Ivashkovich},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203636763909054},
  booktitle={Arkiv for Matematik},
  volume={52},
  number={1},
  pages={149-173},
  year={2012},
}
Sergey Ivashkovich. Banach analytic sets and a non-linear version of the Levi extension theorem. 2012. Vol. 52. In Arkiv for Matematik. pp.149-173. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203636763909054.
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