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This article is cited in 4 scientific papers (total in 4 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 $\Gamma_\nu$, $\nu=1,2,\dots,q$, 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 $w^{-1}(\Gamma_\nu)\cap\{z:|z|\le r\}$, $\nu=1,2,\dots,q$. 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.
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
Linking options:
https://www.mathnet.ru/eng/sm2317https://doi.org/10.1070/SM1982v042n02ABEH002250 https://www.mathnet.ru/eng/sm/v156/i2/p179
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Abstract page: | 280 | Russian version PDF: | 110 | English version PDF: | 10 | References: | 39 |
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