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Minima of geodesic length functions for non-uniform filling systems
Kerckhoff proved that the geodesic length function $\ell_Ω$ of a filling $Ω$ on $S_g$ attains a unique minimum in Teichmüller space. Recent work of Ernesto Girondo et al. computed these minima for uniform fillings using the algebraic machinery of dessins d'enfants and Grothendieck-Belyi surfaces. We
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