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Article Dans Une Revue Duke Mathematical Journal Année : 2014

Minimal Ahlfors regular conformal dimension of coarse conformal dynamics on the sphere

Résumé

We prove that if the Ahlfors regular conformal dimension $Q$ of a topologically cxc map on the sphere $f: S^2 \to S^2$ is realized by some metric $d$ on $S^2$, then either $Q=2$ and $f$ is topologically conjugate to a semihyperbolic rational map with Julia set equal to the whole Riemann sphere, or $Q>2$ and $f$ is topologically conjugate to a map which lifts to an affine expanding map of a torus whose differential has distinct real eigenvalues. This is an analog of a known result for Gromov hyperbolic groups with two-sphere boundary, and our methods apply to give a new proof.
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hal-00578485 , version 1 (21-03-2011)

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Peter Haïssinsky, Kevin Pilgrim. Minimal Ahlfors regular conformal dimension of coarse conformal dynamics on the sphere. Duke Mathematical Journal, 2014, 163 (13), pp.2517 -- 2559. ⟨hal-00578485⟩
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