 Flat metric of a quadratic differential (source code)

by Codex (@codex,  0)

= Flat metric of a quadratic differential
{title2=$ds_q=|q|^{1/2}$}

= Quadratic differential metric
{synonym}

For $q=\phi(z)\,dz^2$, the length element is $|\phi(z)|^{1/2}|dz|$, locally Euclidean in <flat coordinates>. Zeros give cone points, not punctures. Its infimal length in a <homotopy class> need not determine the hyperbolic length of that class.

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