Comptes Rendus
Complex Analysis
Tchebotaröv's problem
Comptes Rendus. Mathématique, Volume 341 (2005) no. 7, pp. 405-408.

We give a complete solution to the extremal problem posed by N.G. Tchebotaröv in the mid 1920s, and we establish explicit parametric formulae for the extremals.

Nous donnons une solution complète du problème extrémal ayant posé par N.G. Tchebotarov vers 1920s, et nous établissons des formules explicites paramétriques pour les extrémales.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.08.007

Promarz Tamrazov 1

1 Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska Str. 3, 01601 Kiev, Ukraine
@article{CRMATH_2005__341_7_405_0,
     author = {Promarz Tamrazov},
     title = {Tchebotar\"ov's problem},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {405--408},
     publisher = {Elsevier},
     volume = {341},
     number = {7},
     year = {2005},
     doi = {10.1016/j.crma.2005.08.007},
     language = {en},
}
TY  - JOUR
AU  - Promarz Tamrazov
TI  - Tchebotaröv's problem
JO  - Comptes Rendus. Mathématique
PY  - 2005
SP  - 405
EP  - 408
VL  - 341
IS  - 7
PB  - Elsevier
DO  - 10.1016/j.crma.2005.08.007
LA  - en
ID  - CRMATH_2005__341_7_405_0
ER  - 
%0 Journal Article
%A Promarz Tamrazov
%T Tchebotaröv's problem
%J Comptes Rendus. Mathématique
%D 2005
%P 405-408
%V 341
%N 7
%I Elsevier
%R 10.1016/j.crma.2005.08.007
%G en
%F CRMATH_2005__341_7_405_0
Promarz Tamrazov. Tchebotaröv's problem. Comptes Rendus. Mathématique, Volume 341 (2005) no. 7, pp. 405-408. doi : 10.1016/j.crma.2005.08.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.08.007/

[1] G. Golusin Method of variations in the theory of conform representation. I, Mat. Sb., Volume 19 (1946) no. 61, pp. 203-236 (in Russian)

[2] G. Golusin Geometric Theory of Functions of a Complex Variable, Amer. Math. Soc., Providence, RI, 1969 (transl. from Russian)

[3] H. Grōtzsch Über ein Variationsproblem der konformen Abbildung, Ber. Ferh. Sächs. Akad. Wiss. Leipzig, Volume 82 (1930), pp. 251-263

[4] J. Jenkins Univalent Functions and Conformal Mappings, Inostr. Lit., Moscow, 1962 (Russian transl.)

[5] G. Kuz'mina Covering theorems for functions holomorphic and univalent within a disk, Dokl. Acad. Nauk SSSR, Volume 160 (1965), pp. 25-28 (in Russian)

[6] M. Lavrentieff Sur un probleme de maximum dans la representation conforme, C. R. Acad. Sci. Paris, Volume 191 (1930), pp. 827-829

[7] M. Lavrentyev On the theory of conformal mappings, Trudy Fiz.-Mat. Inst. Akad. Nauk SSSR, Volume 5 (1934), pp. 159-246 (in Russian)

[8] G. Polya Beitrag zur Verallgemeinerung des Verzerrungssatzes auf mehrfach zusammenhängende Gebiete, III, S.-B. Preuss. Akad. Wiss. Berlin (1929), pp. 55-62

[9] Ch. Pommerenke Univalent Functions, Vandenhoeck and Ruprecht, Göttingen, 1975

Cited by Sources:

Comments - Policy