This article is cited in 1 paper

On a class of exceptional sets in the theory of conformal mappings

N. G. Makarov


Abstract: A subset $E$ of the unit circle $\partial\mathbf D$ is called an $L$-set if there exists a function univalent in the disc $\mathbf D$ mapping $E$ to a set of zero linear measure. Metric properties of $L$-sets are studied, and related problems of the radial behavior of Bloch functions are also considered.
Bibliography: 11 titles.

UDC: 517.5

MSC: 30C35, 30C45

Received: 21.06.1988

 English version: Mathematics of the USSR-Sbornik, 1991, 68:1, 19–30

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