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This article is cited in 78 scientific papers (total in 78 papers)
On Liouville's equation, accessory parameters, and the geometry of Teichmüller space for Riemann surfaces of genus 0
P. G. Zograf, L. A. Takhtadzhyan
Abstract:
For the Weil–Petersson metric on the Teichmüller space $T_{0,n}$ of marked Riemann surfaces of genus 0 with $n$ punctures, a potential is constructed in terms of the density of the hyperbolic metric on the corresponding surface (i.e., in terms of a solution of Liouville's equation). It is shown that this potential is a generating function of the accessory parameters of the Fuchsian uniformization of the corresponding Riemann surface. Also, a connection is established between the accessory parameters and the Eichler integrals of Fuchsian groups.
Bibliography: 18 titles.
Received: 01.04.1986
Citation:
P. G. Zograf, L. A. Takhtadzhyan, “On Liouville's equation, accessory parameters, and the geometry of Teichmüller space for Riemann surfaces of genus 0”, Math. USSR-Sb., 60:1 (1988), 143–161
Linking options:
https://www.mathnet.ru/eng/sm1767https://doi.org/10.1070/SM1988v060n01ABEH003160 https://www.mathnet.ru/eng/sm/v174/i2/p147
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Abstract page: | 1079 | Russian version PDF: | 354 | English version PDF: | 74 | References: | 79 |
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