Geodesic
On Liouville's equation, accessory parameters, and the geometry of Teichmüller space for Riemann surfaces of genus 0
Sbornik. Mathematics, Tome 60 (1988) no. 1, pp. 143-161 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the Weil–Petersson metric on the Teichmüller space $T_{0,n}$ of marked Riemann surfaces of genus 0 with $n$ punctures, a potential is constructed in terms of the density of the hyperbolic metric on the corresponding surface (i.e., in terms of a solution of Liouville's equation). It is shown that this potential is a generating function of the accessory parameters of the Fuchsian uniformization of the corresponding Riemann surface. Also, a connection is established between the accessory parameters and the Eichler integrals of Fuchsian groups. Bibliography: 18 titles. 
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P. G. Zograf; L. A. Takhtadzhyan. On Liouville's equation, accessory parameters, and the geometry of Teichmüller space for Riemann surfaces of genus 0. Sbornik. Mathematics, Tome 60 (1988) no. 1, pp. 143-161. http://geodesic.mathdoc.fr/item/SM_1988_60_1_a8/

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