An Ansatz for the Poincaré metric on compact Riemann surfaces is proposed. This implies that the Liouville equation reduces to an equation resembling a nonchiral analogous of the higher genus relationships (KP equation) arising within the framework of Schottky's problem solution. This approach connects uniformization (Fuchsian groups) and moduli space theories with KP hierarchy. Besides its mathematical interest, the Ansatz has some applications within the framework of quantum Riemann surfaces arising in 2D gravity.
LIOUVILLE EQUATION AND SCHOTTKY PROBLEM
MATONE, MARCO
1995
Abstract
An Ansatz for the Poincaré metric on compact Riemann surfaces is proposed. This implies that the Liouville equation reduces to an equation resembling a nonchiral analogous of the higher genus relationships (KP equation) arising within the framework of Schottky's problem solution. This approach connects uniformization (Fuchsian groups) and moduli space theories with KP hierarchy. Besides its mathematical interest, the Ansatz has some applications within the framework of quantum Riemann surfaces arising in 2D gravity.File in questo prodotto:
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