### Abstract

Let f : (M, p) → (M′, p′) be a formal biholomorphic mapping between two germs of real analytic hypersurfaces in ℂ^{n}, p′ = f(p). Assuming the source manifold to be minimal at p, we prove the convergence of the so-called reflection function associated to f. As a consequence, we derive the convergence of formal biholomorphisms between real analytic minimal holomorphically nondegenerate hypersurfaces. Related results on partial convergence of formal biholomorphisms are also obtained.

Original language | English |
---|---|

Pages (from-to) | 343-359 |

Number of pages | 17 |

Journal | Mathematical Research Letters |

Volume | 7 |

Issue number | 2-3 |

Publication status | Published - 2000 |

Externally published | Yes |

### Fingerprint

### Keywords

- Artin approximation theorem
- Cauchy estimates
- Formal mapping
- Holomorphic non-degeneracy
- Real analytic hypersurfaces

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematical Research Letters*,

*7*(2-3), 343-359.

**Formal biholomorphic maps of real analytic hypersurfaces.** / Mir, Nordine.

Research output: Contribution to journal › Article

*Mathematical Research Letters*, vol. 7, no. 2-3, pp. 343-359.

}

TY - JOUR

T1 - Formal biholomorphic maps of real analytic hypersurfaces

AU - Mir, Nordine

PY - 2000

Y1 - 2000

N2 - Let f : (M, p) → (M′, p′) be a formal biholomorphic mapping between two germs of real analytic hypersurfaces in ℂn, p′ = f(p). Assuming the source manifold to be minimal at p, we prove the convergence of the so-called reflection function associated to f. As a consequence, we derive the convergence of formal biholomorphisms between real analytic minimal holomorphically nondegenerate hypersurfaces. Related results on partial convergence of formal biholomorphisms are also obtained.

AB - Let f : (M, p) → (M′, p′) be a formal biholomorphic mapping between two germs of real analytic hypersurfaces in ℂn, p′ = f(p). Assuming the source manifold to be minimal at p, we prove the convergence of the so-called reflection function associated to f. As a consequence, we derive the convergence of formal biholomorphisms between real analytic minimal holomorphically nondegenerate hypersurfaces. Related results on partial convergence of formal biholomorphisms are also obtained.

KW - Artin approximation theorem

KW - Cauchy estimates

KW - Formal mapping

KW - Holomorphic non-degeneracy

KW - Real analytic hypersurfaces

UR - http://www.scopus.com/inward/record.url?scp=0034350196&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034350196&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 343

EP - 359

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 2-3

ER -