This article is cited in 3 papers

Generalized condensers and boundary distortion theorems for conformal mappings

V. N. Dubinin^ab, V. Yu. Kim<sup>a

a</sup> Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok
^b Far Eastern Federal University, Vladivostok

Abstract: In this paper we prove some boundary distortion theorems for the univalent holomorphic functions in the unit disk by the potential theory. In particular, the discrete analogs of the classical statements on the behavior of the logarithmic capacity of the boundary sets under conformal mappings are established.

Key words: condensers, conformal capacity, meromorphic functions, univalent functions, boundary distortion, angular derivative.

UDC: 517.54

MSC: Primary 30C85; Secondary 30C75

Received: 14.05.2013