An open annulus is a domain in the complex plane of the form
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 .
|Date of creation||2013-03-22 13:34:52|
|Last modified on||2013-03-22 13:34:52|
|Last modified by||Wkbj79 (1863)|