Quasisymmetries of Sierpi\'nski carpet Julia sets

By M. Bonk, M. Lyubich, S. Merenkov. 2014

48 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/4a75b100d30aa24766ab0332c62424eb25227976