Analytic regularity of CR maps into spheres

Nordine Mir (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

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 $\C^N$.

Mots clés: Holomorphic extension; CR map; sphere

Domaines: Variables complexes [math.CV]

Nordine Mir. Analytic regularity of CR maps into spheres. Mathematical Research Letters, 2003, 10 (4), pp.447--457. ⟨hal-00261699⟩