摘要：The quasisymmetric uniformization and rigidity are related to the Gromov hyperbolic goemetry. Bonk et.al. discussed the quasisymmetric uniformization for the Sierpinski carpet metric spaces and the quasisymmetric rigidity for the squre Sierpinski carpets and the Schottky sets. Recently, Bonk, Lyubich and Merenkov
discussed the quasisymmetric uniformization and rigidity for the Sierpinski carpet Julia sets of critically finite rational maps. In this talk, we generalized Bonk, Lyubich and Merenkow's results to the critically infinite rational maps, in particular, the semi-hyperbolic rational maps.