PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (232)
Orphanage
Unclass'd
Unproven (519)
Corrections (20)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Very high Entry average rating: No information on entry rating
Hartogs' theorem (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$.



"Hartogs' theorem" is owned by mathcam. [ full author list (2) | owner history (1) ]
(view preamble | get metadata)

View style:

Other names:  Hartogs' Phenomenon

Attachments:
proof of Hartogs' theorem (Proof) by jirka
failure of Hartogs' theorem in one dimension (Example) by jirka
Log in to rate this entry.
(view current ratings)

Cross-references: holomorphic function, connected, compact subset, open set
There are 6 references to this entry.

This is version 7 of Hartogs' theorem, born on 2003-01-10, modified 2008-05-27.
Object id is 3892, canonical name is HartogsTheorem.
Accessed 3775 times total.

Classification:
AMS MSC: 32H02 (Several complex variables and analytic spaces :: Holomorphic mappings and correspondences :: Holomorphic mappings, embeddings and related questions)
Pending Errata and Addenda
None.
[ View all 6 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | prove | add result | add corollary | add example | add (any)