This article is cited in 3 papers

On the covering of radial segments under $p$-valent mappings of a disk and an annulus

V. N. Dubinin^a, V. Yu. Kim<sup>b

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

Abstract: A covering theorem for radial segments is proved for $p$-valent functions in a circular annulus. As a corollary, a similar theorem for $p$-valent functions in a disc is obtained. These results contain many known covering theorems for conformal mappings.

Key words: $p$-valent function, conformal mapping, covering theorem, condenser capacity, dissymmetrization, Riemann surface.

UDC: 517.54

MSC: Primary 30C25; Secondary 30C85

Received: 27.06.2007

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