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The exponent of convergence and a theorem of Astala. (English) Zbl 1046.30007
Summary: We provide bounds on the exponent of convergence of a planar discrete quasiconformal group in terms of the associated dilatation and (a) the Hausdorff dimension of its conical limit set, or (b) the exponent of convergence of an underlying Kleinian group.

MSC:
30C62 Quasiconformal mappings in the complex plane
30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
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