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Mathematics of the USSR-Sbornik, 1978, Volume 34, Issue 5, Pages 593–601
DOI: https://doi.org/10.1070/SM1978v034n05ABEH001329
(Mi sm2549)
 

This article is cited in 2 scientific papers (total in 2 papers)

On the geometric structure of the image of a disk under mappings by meromorphic functions

G. A. Barsegyan
References:
Abstract: In a recent paper by the author a new geometric definition of deficient values for a function $\omega(z)$ meromorphic in $|z|<\infty$ was introduced, and with its aid a connection between the geometric structure of $F_r=\{\omega(z):|z|\leqslant r\}$ and the distribution of values of $\omega(z)$ was established. In the present paper definitions characterizing the structure of $\partial F_r$, more delicately are introduced, and a more detailed study of these connections is carried out. As a by-product a theorem of Miles is obtained as a corollary. This theorem complements, in a sense, Ahlfors' second fundamental theorem of the theory of covering surfaces.
Bibliography: 3 titles.
Received: 07.09.1977
Bibliographic databases:
UDC: 517.54
MSC: Primary 30D35; Secondary 30C30
Language: English
Original paper language: Russian
Citation: G. A. Barsegyan, “On the geometric structure of the image of a disk under mappings by meromorphic functions”, Math. USSR-Sb., 34:5 (1978), 593–601
Citation in format AMSBIB
\Bibitem{Bar78}
\by G.~A.~Barsegyan
\paper On the geometric structure of the image of a~disk under mappings by meromorphic functions
\jour Math. USSR-Sb.
\yr 1978
\vol 34
\issue 5
\pages 593--601
\mathnet{http://mi.mathnet.ru//eng/sm2549}
\crossref{https://doi.org/10.1070/SM1978v034n05ABEH001329}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=486517}
\zmath{https://zbmath.org/?q=an:0384.30014|0415.30019}
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  • https://doi.org/10.1070/SM1978v034n05ABEH001329
  • https://www.mathnet.ru/eng/sm/v148/i1/p35
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
     
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