Institute for Mathematical Sciences
Mario Bonk, Misha Lyubich, Sergei Merenkov
Quasisymmetries of Sierpinski carpet Julia sets
Abstract: We prove that if $\xi$ is a quasisymmetric homeomorphism between Sierpinski carpets that are the Julia sets of postcritically-finite rational maps, then $\xi$ is the restriction of a Mobius transformation to the Julia set. This implies that the group of quasisymmetric homeomorphisms of a Sierpinski carpet Julia set of a postcritically-finite rational map is finite.
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