On the geometric structure of the image of a disk under mappings by meromorphic functions
Sbornik. Mathematics, Tome 34 (1978) no. 5, pp. 593-601
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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.
@article{SM_1978_34_5_a1,
author = {G. A. Barsegyan},
title = {On the geometric structure of the image of a~disk under mappings by meromorphic functions},
journal = {Sbornik. Mathematics},
pages = {593--601},
year = {1978},
volume = {34},
number = {5},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1978_34_5_a1/}
}
G. A. Barsegyan. On the geometric structure of the image of a disk under mappings by meromorphic functions. Sbornik. Mathematics, Tome 34 (1978) no. 5, pp. 593-601. http://geodesic.mathdoc.fr/item/SM_1978_34_5_a1/
[1] G. A. Barsegyan, “Defektnye znacheniya i struktura poverkhnostei nalozheniya”, Izv. AN ArmSSR, XII:1 (1977), 46–53
[2] R. Nevanlinna, Odnoznachnye analiticheskie funktsii, ONTI, Moskva, 1941 | MR
[3] J. Miles, “Bouns on the ratio $n(r,a)/S(r)$ for meromorphic functions”, Trans. Amer. Math. Soc., 162 (1971), 383–393 | DOI | MR