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Mathematics of the USSR-Sbornik, 1988, Volume 60, Issue 1, Pages 143–161
DOI: https://doi.org/10.1070/SM1988v060n01ABEH003160
(Mi sm1767)
 

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
References:
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
Bibliographic databases:
UDC: 517.9
MSC: Primary 30F10, 32G15; Secondary 11F67, 30F35
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
\Bibitem{ZogTak87}
\by P.~G.~Zograf, L.~A.~Takhtadzhyan
\paper On~Liouville's equation, accessory parameters, and the geometry of Teichm\"uller space for Riemann surfaces of genus~0
\jour Math. USSR-Sb.
\yr 1988
\vol 60
\issue 1
\pages 143--161
\mathnet{http://mi.mathnet.ru//eng/sm1767}
\crossref{https://doi.org/10.1070/SM1988v060n01ABEH003160}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=882831}
\zmath{https://zbmath.org/?q=an:0655.32022|0642.32010}
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  • This publication is cited in the following 78 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:1079
    Russian version PDF:354
    English version PDF:74
    References:79
     
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