Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 097, 16 pages      arXiv:2105.11074      https://doi.org/10.3842/SIGMA.2021.097
Contribution to the Special Issue on Mathematics of Integrable Systems: Classical and Quantum in honor of Leon Takhtajan

Liouville Action for Harmonic Diffeomorphisms

Jinsung Park
School of Mathematics, Korea Institute for Advanced Study, 207-43, Hoegiro 85, Dong-daemun-gu, Seoul, 130-722, Korea

Received May 25, 2021, in final form October 27, 2021; Published online November 02, 2021

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.

Key words: quasi-Fuchsian group; Teichmüller space; Liouville action; harmonic diffeomorphism.

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