Proves an if-and-only-if quasiconformal characterization of Schottky sets on the sphere that applies to Sierpiński carpets and gaskets and generalizes Bonk's carpet result without uniform relative separation.
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A criterion and constructions are given for Cantor bubble Julia sets in rational maps with attracting or parabolic fixed points, including high-period cycles, Hausdorff dimension two, and a quasisymmetric equivalence condition to round bubbles.
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Quasiconformal characterization of Schottky sets
Proves an if-and-only-if quasiconformal characterization of Schottky sets on the sphere that applies to Sierpiński carpets and gaskets and generalizes Bonk's carpet result without uniform relative separation.
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Rational maps with Cantor bubble Julia sets
A criterion and constructions are given for Cantor bubble Julia sets in rational maps with attracting or parabolic fixed points, including high-period cycles, Hausdorff dimension two, and a quasisymmetric equivalence condition to round bubbles.