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On Reich Sequence for Uniquely Extremal Quasiconformal Mapping of Teichmüller Type

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Abstract

In this paper, it is shown that there exists a uniquely extremal quasiconformal mapping of Teichmüller type such that it has a normal (or weak) Reich sequence and the limit of the Reich sequence is not a holomorphic function. The answers a question posed by Reich negatively.

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References

  1. Božin V., Lakic N., Marković V., Mateljević M.: Unique extremality. J. Anal. Math. 75, 299–338 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Božin V., Marković V., Mateljević M.: The unique extremality in the tangent space of the universal Teichmüller space. Integral Transform. Spec. Funct. 6, 145–149 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Hayman W.K., Reich E.: On the Teichmüller mappings of the disk. Complex Var. Theor. Appl. 1, 1–12 (1982)

    Article  MATH  Google Scholar 

  4. Mateljević, M.: Unique extremality II, Travaux de la Conférence Internationale d’Analyse Complexe et du 8e Séminaire Roumano-Finlandais (Iassy, 1999). Math. Rep. (Bucur.) 2(52), no. 4, 503–525 (2000)

  5. Mateljević M.: Unique extremality of quasiconformal mappings. J. Anal. Math. 107, 39–63 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Mateljević M.: Quasiconformal maps and Teicmller theory-extremal mappings, overview. Bull. Cl. Sci. Math. Nat. Sci. Math. No. 38, 129–172 (2013)

    MATH  Google Scholar 

  7. Reich E.: A criteria for unique extremality of Teichmüller mappings. Indiana Univ. Math. J. 3, 441–447 (1981)

    Article  MATH  Google Scholar 

  8. Reich E.: On criteria for unique extremality of Teichmüller mappings. Ann. Acad. Sci. Fenn. Ser. A Math. 6, 289–301 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  9. Reich, E.: Extremal extensions from the circle to the disk. In: Quasiconformal Mappings and Analysis, A Collection of Papers Honoring Gehring F. W. Springer, New York, pp. 321–335 (1997)

  10. Reich E.: The unique extremality counterexample. J. Anal. Math. 75, 339–347 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  11. Rudin W.: Real and Complex Analysis. 3rd Edition. McGraw-Hill, New York (1987)

    MATH  Google Scholar 

  12. Yao G.W.: Is there always an extremal Teichmüller mapping. J. Anal. Math. 94, 363–375 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. Yao G.W.: Existence of extremal Beltrami coefficients with nonconstant modulus. Nagoya Math. J. 199, 1–14 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China

    Guowu Yao

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  1. Guowu Yao
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Correspondence to Guowu Yao.

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In Memory of Professor Edgar Reich

The author was supported by the National Natural Science Foundation of China (Grant No. 11271216).

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Yao, G. On Reich Sequence for Uniquely Extremal Quasiconformal Mapping of Teichmüller Type. Results Math 71, 997–1014 (2017). https://doi.org/10.1007/s00025-016-0590-3

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  • DOI: https://doi.org/10.1007/s00025-016-0590-3

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