Thurston obstructions and Ahlfors regular conformal dimension

  title={Thurston obstructions and Ahlfors regular conformal dimension},
  author={Peter H{\"a}ıssinsky and Univ. Provence and Kevin M. Pilgrim},
Let f : S → S be an expanding branched covering map of the sphere to itself with finite postcritical set Pf . Associated to f is a canonical quasisymmetry class G(f) of Ahlfors regular metrics on the sphere in which the dynamics is (non-classically) conformal. We show inf X∈G(f) H.dim(X) ≥ Q(f) = inf Γ {Q ≥ 2 : λ(fΓ,Q) ≥ 1}. The infimum is over all multicurves Γ ⊂ S − Pf . The map fΓ,Q : R → R is defined by fΓ,Q(γ) = ∑ 

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