Siegel Disks Whose Boundaries are Jordan Curves with Positive Area

Abstract

In this paper, the authors construct a univalent function having a relatively compact Siegel disk whose boundary is a Jordan curve of positive area. The construction is based on a general scheme in which Chéritat added Runge’s theorem, to construct a relatively compact Siegel disk and Osgood’s method for constructing a Jordan curve of positive area.

Keywords

Univalent functions / Siegel disks / Runge’s theorem / A Jordan curve of positive area / 37F50

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