## Institute for Mathematical Sciences

## Preprint ims14-01

** 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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