This is a preview of subscription content, log in via an institution to check access.
Literature cited
H. Gröthsch, “Über ein Variationsproblem der konformen Abbildung,” Ber. Verb. Sächs, Acad. Wiss Leipzig, Math.-Phys. Kl.,82, 251–263 (1930).
G. V. Kuz'mina, “The conformal modulus in the family of doubly connected domains not containing a given system of points,” Zap. Nauch. Sem. LOMI,24, 78–147 (1972).
G. V. Kuz'mina, “Estimates of the conformal modulus of a family of domains and covering theorems for schlicht functions,” Zap. Nauch. Sem. LOMI,24, 148–172 (1972).
J. A. Jenkins, “On certain geometrical problems associated with capacity,” Math. Nachr.,39, Nos. 4–6, 349–356 (1969).
M. Tsuji, “Some metrical theorems on Fuchsian groups,: Jpn. J. Math.,19, No. 3, 483–516 (1947).
M. Tsuji, Potential Theory in Modern Function Theory, Tokyo (1959).
R. Kühnau, “Transfiniter Durchmesser, Kapazität und Tschebyschewsche Konstante in der euklidischen, hyberbolischen und elliptischen Geometrie,” J. Reine Angew. Math.,234, 216–220 (1969).
J. A. Jenkins, Univalent Functions and Conformal Mapping, Springer-Verlag, Berlin-Göttingen-Heidelberg (1958).
U. Pirl, “Über die geometrische Gestalt eines Extremalkontinuums aus der Theorie der konformen Abbildung,” Math. Nachr.,39, Nos. 4–6, 297–312 (1969).
M. A. Lavrent'ev, “On the theory of conformal mappings,” Tr. Fiz.-Mat. Inst., Akad. Nauk SSSR,5, 195–199 (1934).
G. M. Goluzin, Geometric Theory of Functions of Complex Variable [in Russian], Nauka, Moscow (1966).
J. A. Jenkins, “On certain problems of minimal capacity,” Illinois J. Math.,10, No. 3, 460–465 (1966).
H. Wittich, Newest Research on Univalent Analytic Functions [Russian translation], Fizmatgiz, Moscow (1960).
G. V. Kuz'mina, Estimates of the transfinite diameter of a family of continua and covering theorems for schlicht functions,” Tr. Mat. Inst. im V. A. Steklova Akad. Nauk SSSR,94, 47–65 (1968).
J. A. Jenkins, “Some uniqueness results in the theory of symmetrization,” Ann. Math.,61, No. 1, 106–115 (1955).
J. A. Jenkins, “On Bieberbach—Eilenberg functions, II,” Trans. Am. Math. Soc.,78, No. 2, 510–515 (1955).
G. V. Kuz'mina, “Extremal properties of the hyperbolic transfinite diameter and univalent functions in an annulus,” Tr. Mat. Inst. im. V. A. Steklova Akad. Nauk SSSR,94, 66–78 (1968).
P. R. Garanbedian and M. Schiffer, “A coefficient inequality for schlicht functions,” Ann. Math.,61, No. 1, 116–136 (1955).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Mathematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 44, pp. 41–92, 1974.
Rights and permissions
About this article
Cite this article
Kuz'mina, G.V. Some geometric problems connected with hyperbolic capacity. J Math Sci 8, 662–704 (1977). https://doi.org/10.1007/BF01084041
Issue Date:
DOI: https://doi.org/10.1007/BF01084041