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Quasisymmetric geometry of Sierpiński carpet Julia sets

Volume 244 / 2019

Weiyuan Qiu, Fei Yang, Jinsong Zeng Fundamenta Mathematicae 244 (2019), 73-107 MSC: Primary 37F45; Secondary 37F10. DOI: 10.4064/fm494-12-2017 Published online: 7 September 2018

Abstract

In this paper, the main focus is on the Sierpiński carpet Julia sets of rational maps with non-recurrent critical points. We study the uniform quasicircle property of the peripheral circles, the relatively separated property of the peripheral circles and the locally porous property of these carpets. We also establish some quasisymmetric rigidities of these carpets, which generalizes the main results of Bonk–Lyubich–Merenkov (2016) to the postcritically infinite case. In the end we give a strategy to construct a class of postcritically infinite rational maps whose Julia sets are quasisymetrically equivalent to some round carpets.

Authors

  • Weiyuan QiuSchool of Mathematical Sciences
    Fudan University
    Shanghai 200433, P.R. China
    e-mail
  • Fei YangDepartment of Mathematics
    Nanjing University
    Nanjing 210093, P.R. China
    e-mail
  • Jinsong ZengSchool of Mathematics and Information Science
    Guangzhou University
    Guangzhou 510006, P.R. China
    e-mail

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