Liouville Action for Harmonic Diffeomorphisms

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• ISSN: 1815-0659
• Main Author: Park, Jinsung
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211430
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Liouville Action for Harmonic Diffeomorphisms. Jinsung Park. SIGMA 17 (2021), 097, 16 pages

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 ≥ 2. We derive the variational formula of this Liouville action for harmonic diffeomorphisms when the source Riemann surfaces vary with a fixe...