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Mat. Sb. (N.S.), 1981, Volume 114(156), Number 2, Pages 179–225 (Mi msb2317)  

This article is cited in 3 scientific papers (total in 3 papers)

On the geometry of meromorphic functions

G. A. Barsegyan


Abstract: This paper establishes various propositions characterizing the geometric behavior of meromorphic functions $w(z)$ in $|z|<\infty$. “Distortion” theorems for these functions form a basis for the arguments. Namely, a finite number of nice curves $\Gamma_\nu$, $\nu=1,2,…,q$, in the $w$-plane are considered (in particular, $\Gamma_1$ may be a straight line) and information is obtained about the lengths $L(r, \Gamma_\nu)$ of the sets $w^{-1}(\Gamma_\nu)\capż:|z|\le r\}$, $\nu=1,2,…,q$. Qualitatively, the main result is as follows: on some sequence $r_n\to\infty$
\begin{equation} \sum^q_{\nu=1}L(r, \Gamma_\nu)\le KrA(r), \tag{1} \end{equation}
where $K$ is an absolute constant, and $A(r)$ is the Ahlfors characteristic.
Bibliography: 29 titles.

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English version:
Mathematics of the USSR-Sbornik, 1982, 42:2, 155–196

Bibliographic databases:

UDC: 517.53
MSC: Primary 30D30, 30D35; Secondary 30C99, 30F99
Received: 01.08.1979

Citation: G. A. Barsegyan, “On the geometry of meromorphic functions”, Mat. Sb. (N.S.), 114(156):2 (1981), 179–225; Math. USSR-Sb., 42:2 (1982), 155–196

Citation in format AMSBIB
\Bibitem{Bar81}
\by G.~A.~Barsegyan
\paper On~the~geometry of~meromorphic functions
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 114(156)
\issue 2
\pages 179--225
\mathnet{http://mi.mathnet.ru/msb2317}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=609289}
\zmath{https://zbmath.org/?q=an:0484.30021|0457.30027}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 42
\issue 2
\pages 155--196
\crossref{https://doi.org/10.1070/SM1982v042n02ABEH002250}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. A. Barsegyan, “A proximity property of the $a$-points of meromorphic functions”, Math. USSR-Sb., 48:1 (1984), 41–63  mathnet  crossref  mathscinet  zmath
    2. Barsegian G. Yang C., “A New Property of Meromorphic Functions and its Applications”, Analysis and Applications - ISAAC 2001, International Society for Analysis, Applications and Computation, 10, ed. Begehr H. Gilbert R. Wong M., Springer, 2003, 109–120  crossref  mathscinet  isi
    3. Barsegian G., “Gamma-Lines of Polynomials and a Problem by Erdos-Herzog-Piranian”, Topics in Analysis and its Applications, NATO Science Series, Series II: Mathematics, Physics and Chemistry, 147, eds. Barsegian G., Behehr H., Springer, 2004, 119–122  crossref  mathscinet  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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