On the minimal distance between elliptic fixed points for geometrically-finite Fuchsian groups

Let $Γ$ be a geometrically-finite Fuchsian group acting on the upper half plane $\hh.$ Let $\E$ denote the set of elliptic fixed points of $Γ$ in $\hh.$ We give a lower bound on the minimal hyperbolic distance between points in $\E.$ Our bound depends on a universal constant and the length of the smallest closed geodesic on $Γ\backslash \hh.$

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