Abstract
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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This research is supported in part by the grant ANR-10-BLAN-0118.
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Ivashkovich, S. Banach analytic sets and a non-linear version of the Levi extension theorem. Ark Mat 52, 149–173 (2014). https://doi.org/10.1007/s11512-013-0180-5
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DOI: https://doi.org/10.1007/s11512-013-0180-5