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Boundary behavior of the riemann mapping function of asymptotically conformal curves

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References

  1. Ahlfors, L.: Untersuchungen zur Theorie der konformen Abbildungen und der ganzen Funktionen. Acta Soc. Sci. Fenn. (N.S.) A1 (1930)

  2. Becker, J., Pommerenke, Ch.: Über die quasikonforme Fortsetzung schlichter Funktionen. Math. Z.161, 69–80 (1978)

    Google Scholar 

  3. Gaier, D.: Estimates of conformal mappings near the boundary. Indiana Univ. Math. J.21, 581–595 (1972)

    Google Scholar 

  4. Jenkins, J.A., Oikawa, K.: On results of Ahlfors and Hayman. Illinois J. Math.15, 664–671 (1971)

    Google Scholar 

  5. John, F., Nirenberg, L.: On functions of bounded mean oscillation. Comm. Pure Appl. Math.14, 415–426 (1961)

    Google Scholar 

  6. Lesley, F.D.: Hölder continuity of conformal mappings at the boundary via the strip method. Indiana Univ. Math. J. (to appear)

  7. Lesley, F.D., Warschawski, S.E.: On conformal mappings with derivative in VMOA. Math. Z.158, 275–283 (1978)

    Google Scholar 

  8. Lesley, F.D., Warschawski, S.E.: Oscillation on vertical crosscuts in the conformal mapping of infinite strips. J. London Math. Soc. (to appear)

  9. Lorentz, G.G.: Approximation of Functions. New York: Holt, Rinehart and Winston 1966

    Google Scholar 

  10. Pelikh, V.I.: Modulus of continuity of solutions of Plateau Problem. Mat. Zametki26, 561–573 (1979) [Russian]. Engl. Transl.: Math. Notes26, 770–777 (1979)

    Google Scholar 

  11. Pommerenke, Ch.: Univalent Functions. Göttingen: Vandenhoek und Ruprecht 1975

    Google Scholar 

  12. Pommerenke, Ch.: On univalent functions, Bloch functions and VMOA. Math. Ann.236, 199–208 (1978)

    Google Scholar 

  13. Rodin, B.: The method of extremal length. Bull. Amer. Math. Soc.80, 587–606 (1974)

    Google Scholar 

  14. Rodin, B., Warschawski, S.E.: On the derivative of the Riemann mapping function near a boundary point and the Visser-Ostrowski problem. Math. Ann.248, 125–137 (1980)

    Google Scholar 

  15. Warschawski, S.E.: On conformal mapping of infinite strips. Trans. Amer. Math. Soc.51, 280–335 (1942)

    Google Scholar 

  16. Warschawski, S.E.: On differentiability at the boundary in conformal mapping. Proc. Amer. Math. Soc.12, 614–620 (1961)

    Google Scholar 

  17. Warschawski, S.E.: On Hölder continuity at the boundary in conformal mapping. J. Math. Mech.18, 423–428 (1968)

    Google Scholar 

  18. Weiss, M., Zygmund, A.: A note on smooth functions, Indag. Math.21, 52–58 (1959)

    Google Scholar 

  19. Zygmund, A.: Smooth functions. Duke Math. J.12, 47–76 (1945)

    Google Scholar 

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Research partially supported by the National Science Foundation.

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Lesley, F.D., Warschawski, S.E. Boundary behavior of the riemann mapping function of asymptotically conformal curves. Math Z 179, 299–323 (1982). https://doi.org/10.1007/BF01215333

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