Liouville Action for Harmonic Diffeomorphisms

Abstract

In this paper, we introduce a Liouville action for a harmonic diffeomorphism from a compact Riemann surface to a compact hyperbolic Riemann surface of genus $g\ge 2$. We derive the variational formula of this Liouville action for harmonic diffeomorphisms when the source Riemann surfaces vary with a fixed target Riemann surface.

References in corpus (2)

• On the renormalized volume of hyperbolic 3-manifolds
• Liouville action and Holography on quasi-Fuchsian deformation spaces