= Conformal invariance of extremal length
{title2=$\lambda(f\Gamma,f(\Omega))=\lambda(\Gamma,\Omega)$}
For a <conformal map> $f$ and a <conformal metric> $\rho$ on its image, the pullback density is $\rho(f(z))|f'(z)|$. The <change of variables> formula preserves its metric <area>, and the <chain rule> preserves the length of each corresponding curve. Applying this to $f$ and its inverse proves the title equality. This allows <extremal length> computations on rectangles, discs and annuli to be transported to other domains.
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