Definition:Teichmüller Annulus

Definition
Let $R \in \R_{>0}$.

The set:
 * $A := \C \setminus \paren {\closedint{-1} 0 \cup \hointr R {+\infty} }$

is a Teichmüller annulus.

The modulus of $A$ is denoted $\map \Lambda R$.

Also known as
A Teichmüller annulus is also sometimes found referred to as a Teichmüller extremal domain.

Also see

 * 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 $\cmod z = R$, the Teichmüller annulus has the greatest modulus.


 * Definition:Grötzsch Annulus: a related concept