Definition:Teichmüller Annulus

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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.


Source of Name

This entry was named for Oswald Teichmüller.


Sources