= Hyperbolic derivative density
{title2=$H_g(z)=2|g'(z)|/(1-|g(z)|^2)$}
For a nonconstant <holomorphic map> into the <unit disc>, the displayed density pulls the target <hyperbolic metric> back to the source Euclidean coordinate. It is not the operator norm between two hyperbolic tangent spaces, which additionally divides by the source metric density. Away from <ramification points> $\Delta\log H_g=H_g^2$; a <ramification point> of <multiplicity> $m$ adds $2\pi m$ times its point mass to the distributional <Laplacian>.
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