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Inequalities on the inner radius of univalency and the norm of pre-Schwarzian derivative

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Abstract

In this paper, we get a lower bound of inner radius of univalency of Schwarzian derivative by means of the norm of pre-Schwarzian derivative. Furthermore, we apply the theory of Universal Teichmuller Space to explain its geometric meaning which shows the relationship between the inner radius in Universal Teichmuller Space embedded by Schwarzian derivative and the norm defined in Universal Teichmuller Space embedded by pre-Schwarzian derivative.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, CAS, Beijing, 100190, P. R. China

    Tao Cheng

  2. Department of Mathematics, Jiangxi Normal University, Nanchang, 330027, P. R. China

    Tao Cheng

  3. Business Information Management School, Shanghai Institute of Foreign Trade, Shanghai, 201600, P. R. China

    Yue Ming Kang

  4. School of Mathematical Sciences, Fudan University, Shanghai, 200433, P. R. China

    Ji Xiu Chen

Authors
  1. Tao Cheng
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  2. Yue Ming Kang
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  3. Ji Xiu Chen
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Corresponding author

Correspondence to Tao Cheng.

Additional information

Supported by China Postdoctoral Science Foundation funded project (No. 20080430571) and Jiangxi Educational Bureau Foundation (No. GJJ08163)

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Cheng, T., Kang, Y.M. & Chen, J.X. Inequalities on the inner radius of univalency and the norm of pre-Schwarzian derivative. Acta. Math. Sin.-English Ser. 25, 59–64 (2009). https://doi.org/10.1007/s10114-008-6519-3

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  • DOI: https://doi.org/10.1007/s10114-008-6519-3

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