Analytic regularity of CR maps into spheres
Résumé
Let $M\subset \C^N$ be a connected real-analytic hypersurface and $\S\subset \C^{N'}$ the unit real sphere, $N'> N\geq 2$. Assume that $M$ does not contain any complex-analytic hypersurface of $\C^N$ and that there exists at least one strongly pseudoconvex point on $M$. We show that any CR map $f\colon M\to \S$ of class $\6C^{N'-N+1}$ extends holomorphically to a neighborhood of $M$ in $\C^N$.
Domaines
Variables complexes [math.CV]
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