Geodesic
On~Liouville's equation, accessory parameters, and the geometry of Teichm\"uller space for Riemann surfaces of genus~0
Sbornik. Mathematics, Tome 60 (1988) no. 1, pp. 143-161

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. 
@article{SM_1988_60_1_a8,
     author = {P. G. Zograf and L. A. Takhtadzhyan},
     title = {On~Liouville's equation, accessory parameters, and the geometry of {Teichm\"uller} space for {Riemann} surfaces of genus~0},
     journal = {Sbornik. Mathematics},
     pages = {143--161},
     publisher = {mathdoc},
     volume = {60},
     number = {1},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_60_1_a8/}
}
TY  - JOUR
AU  - P. G. Zograf
AU  - L. A. Takhtadzhyan
TI  - On~Liouville's equation, accessory parameters, and the geometry of Teichm\"uller space for Riemann surfaces of genus~0
JO  - Sbornik. Mathematics
PY  - 1988
SP  - 143
EP  - 161
VL  - 60
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1988_60_1_a8/
LA  - en
ID  - SM_1988_60_1_a8
ER  - 
%0 Journal Article
%A P. G. Zograf
%A L. A. Takhtadzhyan
%T On~Liouville's equation, accessory parameters, and the geometry of Teichm\"uller space for Riemann surfaces of genus~0
%J Sbornik. Mathematics
%D 1988
%P 143-161
%V 60
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1988_60_1_a8/
%G en
%F SM_1988_60_1_a8
P. G. Zograf; L. A. Takhtadzhyan. On~Liouville's equation, accessory parameters, and the geometry of Teichm\"uller 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/