Quasisymmetries of Sierpi\'nski carpet Julia sets
Abstract
We prove that if is a quasisymmetric homeomorphism between Sierpi\'nski carpets that are the Julia sets of postcritically-finite rational maps, then 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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