Tchebotaröv’s extremal problem

Promarz Tamrazov

Open Mathematics (2005)

  • Volume: 3, Issue: 4, page 591-605
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Promarz Tamrazov. "Tchebotaröv’s extremal problem." Open Mathematics 3.4 (2005): 591-605. <http://eudml.org/doc/268910>.

@article{PromarzTamrazov2005,
abstract = {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.},
author = {Promarz Tamrazov},
journal = {Open Mathematics},
keywords = {30(C,D,E); 31(A,B,C); 33E, 39B},
language = {eng},
number = {4},
pages = {591-605},
title = {Tchebotaröv’s extremal problem},
url = {http://eudml.org/doc/268910},
volume = {3},
year = {2005},
}

TY - JOUR
AU - Promarz Tamrazov
TI - Tchebotaröv’s extremal problem
JO - Open Mathematics
PY - 2005
VL - 3
IS - 4
SP - 591
EP - 605
AB - 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.
LA - eng
KW - 30(C,D,E); 31(A,B,C); 33E, 39B
UR - http://eudml.org/doc/268910
ER -

References

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  1. [1] G.M. Golusin: “Method of variations in the theory of conform representation”, I, Mat. Sb., Vol. 19(61), (1946), pp. 203–236, (in Russian). Zbl0063.01670
  2. [2] G.M. Golusin: Geometric Theory of Functions of a complex Variable, AMS, Rhode Island, 1969 (transl. from Russian). 
  3. [3] H. Grötzsch, “Über ein Variationsproblem der konformen Abbildung”, Ber. Ferch. Sächs. Akad. Wiss. Leipzig, Vol. 82, (1930), pp. 251–263. 
  4. [4] J.A. Jenkins: Univalent functions and conformal mappings, Inostr. Lit, Moscow, 1962, (Russian transl.). 
  5. [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. [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. [7] M.A. Lavrentieff, “Sur un probleme de maximum dans la representation conforme”, C. R. Acad. Sci. Paris, Vol. 191, (1930), pp. 827–829. Zbl56.0299.02
  8. [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. [9] R. Nevanlinna: Uniformisierung, Inostr. Lit., Moscow, 1955, (Russian transl.). 
  10. [10] G. Polya: Beitrag zur Verallgemeinerung des Verzerrungssatzes auf mehrfach zusammenhängende Gebiete, III, S.-B. Preuss. Akad. Wiss, Berlin, 1929, pp. 55–62. Zbl55.0209.03
  11. [11] Ch. Pommerenke: Univalent Functions, Vandenhoeck and Ruprecht, Göttingen, 1975. 
  12. [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. [13] P.M. Tamrazov: Tchebotaröv’s extremal problem, Kiev, 2004; (Prepr./National Acad. Sci. of Ukraine. Inst. of Math.; 2004.9). 
  14. [14] P. Tamrazov: “Tchebotaröv’s problem”, C. R. Acad. Sci. Paris, Ser. I, (to be published). Zbl1096.30021

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