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References
[A]Ahlfors, L.,Lectures on Quasiconformal Mappings. Van Nostrand, 1966.
[B]Beardon, A. F.,The Geometry of Discrete Groups. Springer-Verlag, 1983.
[BFH]Bielefeld, B., Fischer, Y. &Hubbard, J. H., The classification of critically preperiodic polynomials as dynamical systems.J. Amer. Math. Soc., 5 (1992), 721–762.
[G]Gunning, R.,Lectures on Riemann Surfaces. Mathematical Notes, Princeton University, Press, 1966.
[H]Hubbard, J. H.,Sur les sections analytiques de la courbe universelle de Teichmüller. Mem. Amer. Math. Soc., 166, 1976.
[H-M]Hubbard, J. H. &Masur, H., Quadratic differentials and foliations.Acta Math., 142 (1979), 221–274.
[J]Jenkins, J. A., On the existence of certain general extremal metrics.Ann. of Math., 66 (1957), 440–453.
[O]Ohtsuka, M.,Dirichlet Problem, Extremal Length and Prime Ends. Van Nostrand Reinhold Math. Stud., 22, 1970.
[R]Royden, H., Automorphisms and isometries of Teichmüller space, inAdvances in the Theory of Riemann Surfaces, pp. 369–383. Ann. of Math. Stud., 66. Princeton University Press, 1971.
[S]Strebel, K.,On Quadratic Differentials and Extremal Quasiconformal Mappings. Lecture Notes, University of Minnesota, 1967.
[T1]Thurston, W.,Lecture Notes. Princeton University.
[T2]Thurston, W.,Lecture Notes. CBMS Conference, University of Minnesota at Duluth, 1983.
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We thank the NSF for support under grant DMS 83-01564, and the Mittag-Leffler Institute for hospitality during the preparation of this paper
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Douady, A., Hubbard, J.H. A proof of Thurston's topological characterization of rational functions. Acta Math. 171, 263–297 (1993). https://doi.org/10.1007/BF02392534
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DOI: https://doi.org/10.1007/BF02392534