Conformal metric (source code)

= Conformal metric
{title2=$ds_\rho=\rho|dz|$}

In a <holomorphic coordinate>, a length element $\rho(z)|dz|$. <Smooth> positive densities define ordinary <Riemannian metrics>; <extremal length> also permits nonnegative measurable densities with finite positive area $\int\rho^2\,dx\,dy$.