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 
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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     title = {On~Liouville's equation, accessory parameters, and the geometry of {Teichm\"uller} space for {Riemann} surfaces of genus~0},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_60_1_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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