Mathematical Notes

, Volume 84, Issue 5–6, pp 751–755 | Cite as

Majorization principles for meromorphic functions

  • V. N. Dubinin


Supplements to the Lindelöf principle on the behavior of Green’s function and the Nevanlinna principle on the behavior of the harmonic measure under meromorphic maps are proposed; these supplements go back to Mityuk’s work on the change of the inner radius of a domain under the action of regular functions.

Key words

Lindelöf principle Nevanlinna majorization principle meromorphic function harmonic measure Green’s function subharmonic function 


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  1. 1.
    S. Stoilow, Teoria functiilor de o variabila complexa, Vol. 2: Functii armonice. Suprafete Riemanniene (Editura Academiei Republicii Populare Romîne, Bucharest 1958; Inostr. Lit., Moscow, 1962).Google Scholar
  2. 2.
    G. M. Goluzin, Geometric Theory of Functions of a Complex Variable (Nauka, Moscow, 1966) [in Russian].Google Scholar
  3. 3.
    V. N. Dubinin and M. Vuorinen, “Robin functions and distortion theorems for regular mappings,” in Reports in Mathematics (Univ. of Helsinki, Helsinki, 2007), Preprint 454.Google Scholar
  4. 4.
    I. P. Mityuk, “The symmetrization principle for multiply connected domains,” Dokl. Akad. Nauk SSSR 157(2), 268–270 (1964).MathSciNetGoogle Scholar
  5. 5.
    I. P. Mityuk, “The principle of symmetrization for multiply connected regions and certain of its applications,” Ukr. Mat. Zh. 17(4), 46–54 (1965).zbMATHCrossRefGoogle Scholar
  6. 6.
    I. P. Mityuk, Symmetrization Methods and Their Applications to Geometric Function Theory: An Introduction to Symmetrization Methods (Kubanskii Gos. Univ., Krasnodar, 1980) [in Russian].Google Scholar
  7. 7.
    I. P. Mityuk, Application of Symmetrization Methods to Geometric Function Theory (Kubanskii Gos. Univ., Krasnodar, 1985) [in Russian].Google Scholar
  8. 8.
    I. P. Mityuk, “Estimates of the interior radius (capacity) of some domain (condenser),” Izv. Severo-Kavkaz. Nauchn. Tsentra Vyssh. Shkoly Estestv. Nauk, No. 3, 36–38 (1983).Google Scholar
  9. 9.
    V. N. Dubinin and S. I. Kalmykov, “A majorization principle for meromorphic functions,” Mat. Sb. 198(12), 37–46 (2007) [Sb. Math. 198 (11–12), 1737–1745 (2007)].MathSciNetGoogle Scholar
  10. 10.
    A. L. Lukashov, “Supplements to R. Nevanlinna’s principle for harmonic measures,” Mat. Zametki 84(4), 633–634 (2008) [Math. Notes 84 (4), 589–591 (2008)].CrossRefGoogle Scholar
  11. 11.
    M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations (Springer-Verlag, New York, 1984).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  1. 1.Institute of Applied Mathematics, Far-East DivisionRussian Academy of SciencesMoscowRussia

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