Nevanlinna domains with large boundaries
Complex Variables
2018-08-23 v1
Abstract
We establish the existence of Nevanlinna domains with large boundaries. In particular, these domains can have boundaries of positive planar measure. The sets of accessible points can be of any Hausdorff dimension between and . As a quantitative counterpart of these results, we construct rational functions univalent in the unit disc with extremely long boundaries for a given amount of poles.
Cite
@article{arxiv.1808.07436,
title = {Nevanlinna domains with large boundaries},
author = {Yurii Belov and Alexander Borichev and Konstantin Fedorovskiy},
journal= {arXiv preprint arXiv:1808.07436},
year = {2018}
}