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References
L. V. Ahlfors,The complex analytic structure of the space of closed Riemann surfaces, inAnalytic Functions (R. Nevanlinnaet al., eds.), Princeton Univ. Press, Princeton, 1960, pp. 45–66.
L. V. Ahlfors,Lectures on Quasiconformal Mappings, Van Nostrand, Princeton, 1966. (Reprint: Wadsworth, Belmont, 1987.)
L. V. Ahlfors,Möbius Transformations in Several Dimensions, Lecture Notes, School of Mathematics, Univ. of Minnesota, Minneapolis, 1981.
L. V. Ahlfors and L. Sario,Riemann Surfaces, Princeton Univ. Press, Princeton, 1960.
A. F. Beardon,The Geometry of Discrete Groups, Springer-Verlag, Berlin-Heidelberg-New York, 1983.
C. J. Earle,Reduced Teichmüller spaces, Trans. Amer. Math. Soc.126, (1967), 54–63.
R. Fricke and F. Klein,Vorlesungen über die Theorie der Automorphen Functionen II, B. G. Teubner, Leipzig-Berlin, 1912.
F. P. Gardiner,Teichmüller Theory and Quadratic Differentials, Wiley, New York, 1987.
F. P. Gardiner and H. Masur,Extremal length geometry of Teichmüller space, Complex Variables Theory Appl.16 (1991), 209–237.
L. Keen,On Fricke moduli, inAdvances in the Theory of Riemann Surfaces (L. V. Ahlforset al., eds.), Ann. Math. Studies,66 (1971), 205–224.
L. Keen,On fundamental domains and the Teichmüller modular group, inContributions to Analysis (L. V. Ahlforset al., eds.), Academic Press, New York-London, 1974, pp. 185–194.
L. Keen, H. E. Rauch and A. T. Vasquez,Moduli of punctured tori and the accessory parameter of Lamés equation, Trans. Amer. Math. Soc.255 (1979), 201–230.
L. Keen and C. Series,Pleating coordinates for the Maskit embedding of the Teichmüller space of punctured tori, Topology32 (1993), 719–749.
S. P. Kerkhoff,The asymptotic geometry of Teichmüller space, Topology19 (1980), 23–41.
O. Lehto,Univalent Functions and Teichmüller Spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1987.
A. Marden and K. Strebel,The heights theorem for quadratic differentials on Riemann surfaces, Acta Math.153 (1984), 153–211.
M. Masumoto,Estimates of the euclidean span for an open Riemann surface of genus one, Hiroshima Math. J.22 (1992), 573–582.
M. Masumoto,On the moduli set of continuations of an open Riemann surface of genus one, J. Analyse Math.63 (1994), 287–301.
S. Nag,The Complex Analytic Theory of Teichmüller Spaces, Wiley, New York, 1988.
M. Shiba,The moduli of compact continuations of an open Riemann surface of genus one, Trans. Amer. Math. Soc.301 (1987), 299–311.
M. Shiba,The period matrices of compact continuations of an open Riemann surface of finite genus, inHolomorphic Functions and Moduli I (D. Drasinet al., eds.), Springer-Verlag, New York, 1988, pp. 237–246.
M. Shiba,Conformal embeddings of an open Riemann surface into closed surfaces of the same genus, inAnalytic Function Theory of One Complex Variable (Y. Komatuet al., eds.), Longman Scientific & Technical Essex, 1989, pp. 287–298.
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Masumoto, M. Conformal mappings of a once-holed torus. J. Anal. Math. 66, 117–136 (1995). https://doi.org/10.1007/BF02788820
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DOI: https://doi.org/10.1007/BF02788820