Definition:Teichmüller Annulus

Definition
Let $ R > 0 $. The set
 * $A := \C\setminus ([-1,0]\cup [R,\infty)) $

is called a Teichmüller annulus (or also Teichmüller extremal domain).

The modulus of $A$ is denoted $\Lambda(R)$.

Properties
By the Teichmüller Modulus Theorem, among all annuli that separate the two points $0$ and $-1$ both from $\infty$ and from a point $z\in\C$ with $|z|=R$, the Teichmüller annulus has the greatest modulus.

The Teichmüller annulus is closely related to the Grötzsch annulus.