Liouville Equation And Schottky Problem

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 non chiral analogous of the higher genus relationships (KP equation) arising in 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 in the framework of quantum Riemann surfaces arising in 2D gravity.

12 pages, LaTex file. Expanded version and misprints corrected

References in corpus (3)

• Uniformization theory and 2D gravity I. Liouville action and intersection numbers
• Liouville Theory: Quantum Geometry of Riemann Surfaces
• Quantum Riemann surfaces, 2D gravity and the geometrical origin of minimal models

Cited by in corpus (2)

• Higher genus superstring amplitudes from the geometry of moduli spaces
• The Liouville Geometry of N=2 Instantons and the Moduli of Punctured Spheres