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Quasisymmetries of Sierpiński carpet Julia sets (1403.0392v1)
Published 3 Mar 2014 in math.DS
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.