= Hyperbolic systole
{title2=$\operatorname{sys}_{\rm hyp}(X)$}
The <infimum> of nonconstant closed <geodesic> lengths in curvature $-1$, with value $+\infty$ if there are none. On a <closed surface> with a <hyperbolic metric> this is a positive attained minimum, and a minimizing <geodesic> is simple. For fixed closed <genus> $g\geq2$, a common positive lower bound gives relative compactness in the unmarked <moduli space of Riemann surfaces> by <Mumford's compactness theorem>.
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