Geometrization of postcritically finite branched coverings (revised)
  We study canonical decompositions of postcritically finite branched coverings of the 2-sphere, as defined by K. Pilgrim. We show that every hyperbolic cycle in the decomposition does not have a Thurston obstruction. It is thus Thurston equivalent to a rational map. 
Sylvain Bonnot, Michael Yampolsky
math.DS math.GT