Liouville Equation And Schottky Problem

Details Liouville Equation And Schottky Problem Liouville Equation And Schottky Problem

1993-10-12

arxiv.org/abs/hep-th/9310066v2

Lett.Math.Phys. 33 (1995) 75-86

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, LaTex file. Expanded version and misprints corrected

Scientific paper

10.1007/BF00750813

An Ansatz for the Poincar\'e 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.

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