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arXiv · 1710.10305

Squeezing functions and Cantor Sets

Leandro Arosio·John Erik Fornæss·Nikolay Shcherbina·Erlend Fornæss Wold
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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.

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Leandro Arosio, John Erik Fornæss, Nikolay Shcherbina, Erlend Fornæss Wold. 2017-10-27. Squeezing functions and Cantor Sets. https://arxiv.org/abs/1710.10305

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