Hartogs’ theorem

Let $U\subset {ℂ}^n$ ($n>1$) 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
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