Makarov, N. G. On a class of exceptional sets in the theory of conformal mappings. (Russian) Zbl 0688.30006 Mat. Sb. 180, No. 9, 1171-1182 (1989). Let U be the unit disk. A set \(E\subset \partial U\) is called an L-set if there exists a univalent function in U which maps E to a set of zero linear measure. It is proved that L-sets E satisfy the following condition: for every compact \(F\subset E\) \[ \sum \phi (\ell_{\nu})=\infty, \] where \(\ell_{\nu}\) are the lengths of intervals complementary to F and \[ \phi (t)=t\sqrt{\log (1/t)\log \log \log (1/t)}. \] This \(\phi\) is the best possible. Reviewer: A.E.Eremenko Cited in 1 ReviewCited in 2 Documents MSC: 30C35 General theory of conformal mappings 30C99 Geometric function theory Keywords:boundary distortion of conformal mapping PDFBibTeX XMLCite \textit{N. G. Makarov}, Mat. Sb. 180, No. 9, 1171--1182 (1989; Zbl 0688.30006) Full Text: EuDML