Analytic regularity of CR maps into spheres

Nordine Mir

paper

Analytic regularity of CR maps into spheres

arXiv:math/0310371

Abstract

Let $M$ be a connected real-analytic hypersurface in $\C^N$ and $§$ the unit real sphere in $\C^{N'}$, $N^{'} > N \geq 2$ . 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 $f : M \to §$ of class $C^{N^{'} - N + 1}$ extends holomorphically to a neighborhood of $M$ in $\C^N$.

11 pages