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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 097, 16 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.097 (Mi sigma1779) 		 
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
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DOI: https://doi.org/10.3842/SIGMA.2021.097
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.
Keywords: quasi-Fuchsian group, Teichmüller space, Liouville action, harmonic diffeomorphism.
Funding agency Grant number
Samsung Science and Technology Foundation SSTF-BA1701-02
This work was partially supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1701-02.
Received: May 25, 2021; in final form October 27, 2021; Published online November 2, 2021
Bibliographic databases:
Document Type: Article
MSC: 14H60, 32G15, 53C43, 58E20
Language: English
Citation: Jinsung Park, “Liouville Action for Harmonic Diffeomorphisms”, SIGMA, 17 (2021), 097, 16 pp.
Citation in format AMSBIB
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