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arXiv · 1403.0392

Quasisymmetries of Sierpi\'nski carpet Julia sets

Mario Bonk·Misha Lyubich·Sergei Merenkov
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Abstract

We prove that if $\xi$ is a quasisymmetric homeomorphism between Sierpi\'nski carpets that are the Julia sets of postcritically-finite rational maps, then $\xi$ is the restriction of a M\"obius transformation to the Julia set. This implies that the group of quasisymmetric homeomorphisms of a Sierpi\'nski carpet Julia set of a postcritically-finite rational map is finite.

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Mario Bonk, Misha Lyubich, Sergei Merenkov. 2014-03-03. Quasisymmetries of Sierpi\'nski carpet Julia sets. https://arxiv.org/abs/1403.0392

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