# free analytic boundary arc

###### Definition.

Let $G\subset \u2102$ be a region and let $\gamma $ be a connected^{} subset of $\partial G$ (boundary of $G$), then $\gamma $ is a free analytic boundary arc of
$G$ if for every point $\zeta \in \gamma $ there is a neighbourhood $U$ of
$\zeta $ and
a conformal equivalence $h:\mathbb{D}\to U$ (where $\mathbb{D}$ is the unit disc^{}) such that $h(0)=\zeta $, $h(-1,1)=\gamma \cap U$ and
$h({\mathbb{D}}_{+})=G\cap U$ (where ${\mathbb{D}}_{+}$ is all the points
in the unit disc with non-negative imaginary part).

## References

- 1 John B. Conway. . Springer-Verlag, New York, New York, 1995.

Title | free analytic boundary arc |
---|---|

Canonical name | FreeAnalyticBoundaryArc |

Date of creation | 2013-03-22 14:18:00 |

Last modified on | 2013-03-22 14:18:00 |

Owner | jirka (4157) |

Last modified by | jirka (4157) |

Numerical id | 7 |

Author | jirka (4157) |

Entry type | Definition |

Classification | msc 30-00 |

Classification | msc 54-00 |

Related topic | AnalyticCurve |