# Hartogs’ theorem

Let $U\subset\mathbb{C}^{n}$ ($n>1$) 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 HartogsTheorem 2013-03-22 13:21:57 2013-03-22 13:21:57 mathcam (2727) mathcam (2727) 10 mathcam (2727) Theorem msc 32H02 Hartogs’ Phenomenon