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CR-continuation of arc-analytic maps


Author: Janusz Adamus
Journal: Proc. Amer. Math. Soc. 143 (2015), 4189-4198
MSC (2010): Primary 14P20, 32V10; Secondary 14P10, 32V40, 32V20
Published electronically: July 1, 2015
MathSciNet review: 3373919
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Abstract: Given a set $ E$ in $ \mathbb{C}^m$ and a point $ p\in E$, there is a unique smallest complex-analytic germ $ X_p$ containing $ E_p$, called the holomorphic closure of $ E_p$. We study the holomorphic closure of semialgebraic arc-symmetric sets. Our main application concerns CR-continuation of semialgebraic arc-analytic mappings: A mapping $ f:M\to \mathbb{C}^n$ on a connected real-analytic CR manifold which is semialgebraic arc-analytic and CR on a non-empty open subset of $ M$ is CR on the whole $ M$.


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Additional Information

Janusz Adamus
Affiliation: Department of Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7 – and – Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warsaw, Poland
Email: jadamus@uwo.ca

DOI: https://doi.org/10.1090/proc/12571
Received by editor(s): January 18, 2014
Received by editor(s) in revised form: June 3, 2014
Published electronically: July 1, 2015
Additional Notes: Research was partially supported by Natural Sciences and Engineering Research Council of Canada.
Communicated by: Franc Forstneric
Article copyright: © Copyright 2015 American Mathematical Society