Hyperbolic metric on the punctured disk
= Hyperbolic metric on the punctured disk
{title2=$ds=|dz|/(|z|\log(1/|z|))$}
The <universal covering map> $\tau\mapsto e^{i\tau}$ from the <complex upper half-plane> to the punctured <unit disc> pulls back the metric $|dz|/(|z|\log(1/|z|))$ to $|d\tau|/\operatorname{Im}\tau$. This is its complete curvature-minus-one <hyperbolic metric>, which is different from restricting the ordinary disk metric to the punctured disk.
// Destination: analysis.bigb