Action of the Liouville equation is a generating function for the accessory parameters and the potential of the Weil-Petersson metric on the Teichmüller space
Two theorems on relationship between the Liouville equation \((\partial^ 2/\partial z\partial \bar z)\phi =e^{\phi}\) and geometry of Teichmüller space are announced: (i) If \(\phi\) satisfies the Liouville equation, an explicitly defined integral S(\(\phi)\) is stated to be the generating function for accessory parameters on Teichmüller space. (ii) S is stated to be the potential of the Weil-Peterson metric on that space.
scientific article; zbMATH DE number 3989776