An annulus is the region boundedPlanetmathPlanetmath between two (usually concentric) circles.

An open annulus is a domain in the complex planeMathworldPlanetmath of the form


where w is an arbitrary complex numberMathworldPlanetmathPlanetmath, and r and R are real numbers with 0<r<R. 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 r=0 or R=. (This makes sense for the purposes of the bound on |z-w| 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 w, and r and R are real numbers with 0<r<R.

One can show that two annuli Dw(r,R) and Dw(r,R) are conformally equivalent if and only if R/r=R/r. More generally, the complement of any closed disk in an open disk is conformally equivalent to precisely one annulus of the form D0(r,1).

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