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# From Rubber Bands to Rational Maps Research Report

@inproceedings{Thurston2015FromRB, title={From Rubber Bands to Rational Maps Research Report}, author={Dylan Thurston}, year={2015} }

- Published 2015

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