CR-continuation of arc-analytic maps

Adamus, Janusz

doi:10.1090/proc/12571

CR-continuation of arc-analytic maps
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Proc. Amer. Math. Soc. 143 (2015), 4189-4198 Request permission

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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