# Hartogs’ theorem

Let $U\subset {\u2102}^{n}$ ($n>1$) be an open set, and let $K$ be a compact subset of $U$ such that $U-K$ is connected. Then any holomorphic function^{} on $U-K$ extends uniquely to a holomorphic function on $U$.

Title | Hartogs’ theorem |
---|---|

Canonical name | HartogsTheorem |

Date of creation | 2013-03-22 13:21:57 |

Last modified on | 2013-03-22 13:21:57 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 10 |

Author | mathcam (2727) |

Entry type | Theorem |

Classification | msc 32H02 |

Synonym | Hartogs’ Phenomenon |