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# Mathematical Research Letters

## Volume 10 (2003)

### Number 4

### Analytic regularity of CR maps into spheres

Pages: 447 – 457

DOI: http://dx.doi.org/10.4310/MRL.2003.v10.n4.a4

#### Author

#### Abstract

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