annulus
An open annulus is a domain in the complex plane of the form
where is an arbitrary complex number, and and are real numbers with . Such a set is often called an annular region.
It should be noted that the annulus usually refers to an open annulus.
More generally, one can allow or . (This makes sense for the purposes of the bound on above.) This would make an annulus include the cases of a punctured disc, and some unbounded domains.
Analogously, a closed annulus is a set of the form
where , and and are real numbers with .
One can show that two annuli and are conformally equivalent if and only if . More generally, the complement of any closed disk in an open disk is conformally equivalent to precisely one annulus of the form .
Title | annulus |
---|---|
Canonical name | Annulus1 |
Date of creation | 2013-03-22 13:34:52 |
Last modified on | 2013-03-22 13:34:52 |
Owner | Wkbj79 (1863) |
Last modified by | Wkbj79 (1863) |
Numerical id | 7 |
Author | Wkbj79 (1863) |
Entry type | Definition |
Classification | msc 30-00 |
Synonym | open annulus |
Synonym | annular region |
Related topic | Annulus |
Defines | closed annulus |