Squeezing functions and Cantor Sets
Complex Variables
2017-10-31 v1
Abstract
We construct "large" Cantor sets whose complements resemble the unit disk arbitrarily well from the point of view of the squeezing function, and we construct "large" Cantor sets whose complements do not resemble the unit disk from the point of view of the squeezing function. Finally we show that complements of Cantor sets arising as Julia sets of quadratic polynomials have degenerate squeezing functions, despite of having Hausdorff dimension arbitrarily close to two.
Cite
@article{arxiv.1710.10305,
title = {Squeezing functions and Cantor Sets},
author = {Leandro Arosio and John Erik Fornæss and Nikolay Shcherbina and Erlend Fornæss Wold},
journal= {arXiv preprint arXiv:1710.10305},
year = {2017}
}