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April 2014 Banach analytic sets and a non-linear version of the Levi extension theorem
Sergey Ivashkovich
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Ark. Mat. 52(1): 149-173 (April 2014). DOI: 10.1007/s11512-013-0180-5

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.

Funding Statement

This research is supported in part by the grant ANR-10-BLAN-0118.

Citation

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Sergey Ivashkovich. "Banach analytic sets and a non-linear version of the Levi extension theorem." Ark. Mat. 52 (1) 149 - 173, April 2014. https://doi.org/10.1007/s11512-013-0180-5

Information

Received: 6 April 2012; Revised: 28 November 2012; Published: April 2014
First available in Project Euclid: 30 January 2017

zbMATH: 1314.32016
MathSciNet: MR3175299
Digital Object Identifier: 10.1007/s11512-013-0180-5

Rights: 2013 © Institut Mittag-Leffler

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Vol.52 • No. 1 • April 2014
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