Tchebotaröv’s extremal problem

• Autorzy: Promarz Tamrazov
• Języki publikacji: EN

Abstrakty

EN

We give the complete solution of the extremal problem posed by N.G. Tchebotaröv in 20th of the last century, and we establish explicit parametric formulae for the extremals.

Słowa kluczowe

EN

Tchebotaröv’s problem; conformal mappings; logarithmic capacity; quadratic differentials; Riemann surfaces; graphs; 30(C,D,E); 31(A,B,C); 33E, 39B

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2005
• Tom: 3
• Numer: 4
• Strony: 591-605

Daty

wydano

2005-12-01

online

2005-12-01

Twórcy

autor

Promarz Tamrazov

• National Academy of Sciences of Ukraine

Bibliografia

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• [3] H. Grötzsch, “Über ein Variationsproblem der konformen Abbildung”, Ber. Ferch. Sächs. Akad. Wiss. Leipzig, Vol. 82, (1930), pp. 251–263.
• [4] J.A. Jenkins: Univalent functions and conformal mappings, Inostr. Lit, Moscow, 1962, (Russian transl.).
• [5] S.L. Krushkal, B.N. Apanasov and B.N. Gusevskii: Kleinian groups and uniformisation in examples and problems, Nauka, Novosibirsk, 1981, (in Russian).
• [6] G.V. Kuz’mina: “Covering theorems for functions holomorphic and univalent within a disk”, Dokl. Acad. Nauk SSSR, Vol. 160, (1965), pp. 25–28 (Russian.)
• [7] M.A. Lavrentieff, “Sur un probleme de maximum dans la representation conforme”, C. R. Acad. Sci. Paris, Vol. 191, (1930), pp. 827–829.
• [8] M.A. Lavrentyev: “On the theory of conformal mappings”, Trudy Fiz-Mat. Inst. Akad. Nauk SSSR, Vol. 5, (1934), pp. 159–246, (in Russian).
• [9] R. Nevanlinna: Uniformisierung, Inostr. Lit., Moscow, 1955, (Russian transl.).
• [10] G. Polya: Beitrag zur Verallgemeinerung des Verzerrungssatzes auf mehrfach zusammenhängende Gebiete, III, S.-B. Preuss. Akad. Wiss, Berlin, 1929, pp. 55–62.
• [11] Ch. Pommerenke: Univalent Functions, Vandenhoeck and Ruprecht, Göttingen, 1975.
• [12] P.M. Tamrazov: “Theorems on the covering of lines under a conformal mapping”, Mat. Sb., Vol. 66(108), (1965), pp. 502–524 (Russian).
• [13] P.M. Tamrazov: Tchebotaröv’s extremal problem, Kiev, 2004; (Prepr./National Acad. Sci. of Ukraine. Inst. of Math.; 2004.9).
• [14] P. Tamrazov: “Tchebotaröv’s problem”, C. R. Acad. Sci. Paris, Ser. I, (to be published).

Identyfikatory

DOI

10.2478/BF02475620