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Stable Teichmüller mappings of type (0, 4)

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Abstract

Let X = ℂ\{0, 1} and \(\dot X = X\backslash \left\{ {\hat a} \right\}\). We get a necessary and sufficient condition on the position of \(\hat a\) in X such that \(\dot X\) has stable Teichmüller mappings. Furthermore, we can formulate all these stable Teichmüller mappings. The main result in this paper partially answers a question posed by Kra.

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References

  1. Bers L. An extremal problem for quasiconformal mappings and a theorem by Thurston. Acta Math, 1978, 141: 73–98

    Article  MATH  MathSciNet  Google Scholar 

  2. Imayoshi Y, Taniguchi M. An Introduction to Teichmüller Spaces. Berlin: Springer-Verlag, 1992

    MATH  Google Scholar 

  3. Kra I. On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces. Acta Math, 1981, 146: 231–270

    Article  MATH  MathSciNet  Google Scholar 

  4. Kravetz S. On the geometry of Teichmüller spaces and the structure of their modular groups. Ann Aead Sci Fenn, 1959, 278: 1–35

    MathSciNet  Google Scholar 

  5. Marden A, Strebel K. Pseudo-Anosov Teichmüller mappings. J Anal Math, 1986, 46: 194–220

    Article  MATH  MathSciNet  Google Scholar 

  6. Nag S. The Complex Analytic Theory of Teichmüller Spaces. New York: Wiley, 1988

    MATH  Google Scholar 

  7. Strebel K. Quadratic Differentials. Berlin: Springer-Verlag, 1984

    MATH  Google Scholar 

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Correspondence to Yan Huang.

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Huang, Y., Wu, S. Stable Teichmüller mappings of type (0, 4). Sci. China Math. 54, 1379–1388 (2011). https://doi.org/10.1007/s11425-011-4202-0

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  • DOI: https://doi.org/10.1007/s11425-011-4202-0

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