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
type: Item
instance of: scholarly article
title: 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
zbMATH Open document ID: 0612.32018
DOI: 10.1007/BF01076626
author: Leon A. Takhtajan
author: Peter Zograf
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 31C15
zbMATH DE Number: 3989776
zbMATH Keywords: Liouville equation
zbMATH Keywords: Teichmüller space
zbMATH Keywords: potential of the Weil-Peterson metric
reviewed by: Julian Ławrynowicz
MaRDI profile type: Publication
cites work: Monodromy groups and Poincaré series
cites work: Fourier coefficients of the resolvent for a Fuchsian group.
cites work: Infinite conformal symmetry in two-dimensional quantum field theory
cites work: Some remarks on Teichmüller's space of Riemann surfaces
full work available at URL: https://doi.org/10.1007/bf01076626
OpenAlex ID: W1964065509
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3989776