Conformal cylinder
= Conformal cylinder
{title2=$(\mathbb R/\mathbb Z)\times(0,M)$}
The quotient of a horizontal strip by a horizontal translation. The model $(\mathbb R/\mathbb Z)\times(0,M)$ has <conformal modulus of an annulus> $M$. Averaging horizontal loop lengths and applying <Cauchy-Schwarz inequality> proves that the core-loop <extremal length> equals $1/M$.