Science China Mathematics

, Volume 61, Issue 12, pp 2157–2220 | Cite as

Hyperbolic-parabolic deformations of rational maps

  • Guizhen CuiEmail author
  • Lei Tan


We develop a Thurston-like theory to characterize geometrically finite rational maps, and then apply it to study pinching and plumbing deformations of rational maps. We show that under certain conditions the pinching path converges uniformly and the quasiconformal conjugacy converges uniformly to a semi-conjugacy from the original map to the limit. Conversely, every geometrically finite rational map with parabolic points is the landing point of a pinching path for any prescribed plumbing combinatorics.


rational map geometrically finite hyperbolic parabolic 


37F20 37F45 



This work was supported by National Natural Science Foundation of China (Grant No. 11125106).


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Copyright information

© Science in China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.LAREMAUniversité d’AngersAngersFrance

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