From Rubber Bands to Rational Maps Research Report

  title={From Rubber Bands to Rational Maps Research Report},
  author={Dylan Thurston},
We develop parallel theories of elastic graphs and conformal surfaces with boundary. One one hand, this lets us tell when one rubber band network is looser than another, and on the other hand tell when one conformal surface embeds in another. We apply this to give a new characterization of hyperbolic critically nite rational maps among branched self-coverings of the sphere, by a positive criterion: a branched covering is equivalent to a hyperbolic rational map if and only if there is an elastic… CONTINUE READING

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  • Guizhen Cui, Wenjuan Peng, Tan Lei, Renormalization, wandering Jordan curves of rational maps
  • arXiv:1403.5024,
  • 2014

An algebraic characterization of expanding Thurston maps

  • Peter Haïssinsky, Kevin M. Pilgrim
  • J. Mod. Dyn
  • 2012

Ideal triangulations of pseudo-Anosov mapping tori, Topology and geometry in dimension three

  • Ian Agol
  • Contemp. Math.,
  • 2011

Metric properties of outer space

  • Stefano Francaviglia, Armando Martino
  • Publ. Mat
  • 2011

Critical portraits for postcritically nite polynomials

  • Alfredo Poirier
  • Fund. Math
  • 2009


  • Volodymyr Nekrashevych, Self-similar groups, Mathematical Surveys, Monographs
  • 117, American Mathematical Society, Providence…
  • 2005

Harmonic maps between Riemannian polyhedra

  • M. Gromov
  • Cambridge Tracts in Mathematics,
  • 2001

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