References
J. M. Anderson, K. F. Barth and D. A. Brannan,Research problems in complex analysis, Bull. London Math. Soc.9 (1977), 129–162.
T. Bagby,The modulus of a plane condenser, J. Math. Mech.17 (1967), 315–329.
D. Gaier,Estimates of conformal mappings near the boundary, Indiana Univ. Math. J.21 (1972), 581–595.
H. Grötzsch,Über ein Variationsproblem der konkformen Abbildung, Ber. Verh. sächs, Akad. Wiss. Lipzig, Math.-phys. K1.82 (1930), 251–263.
J. A. Jenkins,On the existence of certain general extremal metrics, Ann. of Math., II. Ser.66 (1957), 440–453.
J. A. Jenkins,Univalent Functions and Conformal Mapping, Springer-Verlag, Berlin-Heidelberg-New York, 1965.
J. A. Jenkins,On a problem concerning harmonic measure, Math. Z.135 (1974), 279–283.
J. G. Krzyż,An extremal length problem and its applications, Proceedings of the NRL Conference on Classical Function Theory, U.S. Government Printing Office, Washington, D.C., 1970, pp. 143–155.
R. Kühnau,Geometrie der konformen Abbildung auf der hyperbolischen und der elliptischen Ebene, VEB Deutscher Verlag der Wissenschaften, Berlin, 1974.
G. V. Kuz’mina,On the conformal modulus in classes of doubly connected domains not containing given systems of points, Zap. Naučn. Sem. LOMI24 (1972), 78–147 (English translation in J. Soviet Math.2 (1974), 618–667).
G. V. Kuz’mina,Estimates of the conformal modulus of a set of domains and covering theorems for univalent functions, Zap. Naučn. Sem. LOMI24 (1972), 148–172 (English translation in J. Soviet Math.2 (1974), 668–685).
F. Leja,Sur les suites de polynômes, les ensembles fermés et la fonction de Green, Ann. Soc. Polon. Math.12 (1934), 57–71.
L. Liao,On a minimax formula of Leja’s, to appear in Kõdai Math. J.
A. C. Schaeffer and D. C. Spencer,Coefficient regions for schlicht functions, Amer. Math. Soc. Colloquium Publ. 35, New York, 1950.
O. Teichmüller,Extremale quasikonforme Abbildungen und quadratische Differentiale, Abh. preuss. Akad. Wiss., Phys.-Math. Kl. 1939, No. 22.
M. Tsuji,Potential Theory in Modern Function Theory, Maruzen Co., Ltd., Tokyo, 1959.
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Liao, L. Certain extremal problems concerning module and harmonic measure. J. Anal. Math. 40, 1–42 (1981). https://doi.org/10.1007/BF02790155
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DOI: https://doi.org/10.1007/BF02790155