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In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R)
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The Fuchsian monodromy problem
Equation 6.2 is just the Liovelle Action, the action principle for the Liouville Field, which is well-known from the familiar conformal gauge.
$$S_L=\frac{c}{96\pi}\int_\mathcal{M}\left(\dot\varphi^2- …