### Abstract

Let M ⊂ ℂ^{N} be a connected real-analytic hypersurface and double-struck S^{2N′-1} ⊂ ℂ^{N′} the unit real sphere, N′ > N ≥ 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 → double-struck S^{2N′-1} of class C^{N′-N+1} extends holomorphically to a neighborhood of M in ℂ^{N}.

Original language | English |
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Pages (from-to) | 447-457 |

Number of pages | 11 |

Journal | Mathematical Research Letters |

Volume | 10 |

Issue number | 4 |

Publication status | Published - Jul 2003 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematical Research Letters*,

*10*(4), 447-457.

**Analytic regularity of CR maps into spheres.** / Mir, Nordine.

Research output: Contribution to journal › Article

*Mathematical Research Letters*, vol. 10, no. 4, pp. 447-457.

}

TY - JOUR

T1 - Analytic regularity of CR maps into spheres

AU - Mir, Nordine

PY - 2003/7

Y1 - 2003/7

N2 - Let M ⊂ ℂN be a connected real-analytic hypersurface and double-struck S2N′-1 ⊂ ℂN′ the unit real sphere, N′ > N ≥ 2. Assume that M does not contain any complex-analytic hypersurface of ℂN and that there exists at least one strongly pseudoconvex point on M. We show that any CR map f : M → double-struck S2N′-1 of class CN′-N+1 extends holomorphically to a neighborhood of M in ℂN.

AB - Let M ⊂ ℂN be a connected real-analytic hypersurface and double-struck S2N′-1 ⊂ ℂN′ the unit real sphere, N′ > N ≥ 2. Assume that M does not contain any complex-analytic hypersurface of ℂN and that there exists at least one strongly pseudoconvex point on M. We show that any CR map f : M → double-struck S2N′-1 of class CN′-N+1 extends holomorphically to a neighborhood of M in ℂN.

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UR - http://www.scopus.com/inward/citedby.url?scp=0141816669&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0141816669

VL - 10

SP - 447

EP - 457

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 4

ER -