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On the locally univalent Bloch constant

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We give a new lower bound of the locally univalent Bloch constant.

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References

  1. L. V. Ahlfors and H. Grunsky,Über die Blochsche Konstante, Math. Z.42 (1937), 671–673.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. Bloch,Les théorèmes de M. Valiron sur les fonctions entières et la théorie de l'uniformisation, Ann. Fac. Sci. Univ. Toulouse III17 (1925), 1–12.

    MathSciNet  Google Scholar 

  3. M. Bonk,On Bloch's constant, Proc. Amer. Math. Soc.110 (1990), 889–894.

    Article  MATH  MathSciNet  Google Scholar 

  4. H. Chen and P. Gauthier,On Bloch's constant, J. Analyse Math.69 (1996), 275–291.

    MATH  MathSciNet  Google Scholar 

  5. M. Heins,On a class of conformal metrics, Nagoya Math. J.21 (1962), 1–60.

    MATH  MathSciNet  Google Scholar 

  6. E. Landau,Der Picard-Schottkysche Satz und die Blochsche Konstanten, Sitz. Preuss. Akad. Wiss. Berlin, Phys-Math. KI (1926), 467–474.

  7. E. Landau,Über die Blochsche Konstante und zwei verwandte Weltkonstanten, Math. Z.30 (1929), 608–643.

    Article  MathSciNet  MATH  Google Scholar 

  8. X. Liu and C. D. Minda,Distortion theorems for Bloch functions, Trans. Amer. Math. Soc.333 (1992), 325–338.

    Article  MATH  MathSciNet  Google Scholar 

  9. C. D. Minda,Bloch constants, J. Analyse Math.41 (1982), 54–84.

    MATH  MathSciNet  Google Scholar 

  10. C. D. Minda,Euclidean, hyperbolic and spherical Bloch constants, Bull. Amer. Math. Soc.6 (1982), 441–444.

    Article  MATH  MathSciNet  Google Scholar 

  11. C. D. Minda,Bloch constants for meromorphic functions, Math. Z.181 (1982), 83–92.

    Article  MATH  MathSciNet  Google Scholar 

  12. H. Yanagihara,On the locally univalent Bloch constant, J. Analyse Math.65 (1995), 1–17.

    MATH  MathSciNet  Google Scholar 

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Correspondence to Huaihui Chen.

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Research supported in part by National Natural Science Foundation of China, #10231010, #10171047, and Grant-in-Aid for Scientific Research, Japan Society for the Promotion of Science (B), #1144048.

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Chen, H., Shiba, M. On the locally univalent Bloch constant. J. Anal. Math. 94, 159–170 (2004). https://doi.org/10.1007/BF02789045

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  • DOI: https://doi.org/10.1007/BF02789045

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