Astala’s Conjecture on Distortion of Hausdorff Measures under Quasiconformal Maps in the Plane
نویسندگان
چکیده
Let E ⊂ C be a compact set, g : C → C be a K-quasiconformal map, and let 0 < t < 2. Let H denote t-dimensional Hausdorff measure. Then H(E) = 0 =⇒ H ′ (gE) = 0 , t′ = 2Kt 2 + (K − 1)t . This is a refinement of a set of inequalities on the distortion of Hausdorff dimensions by quasiconformal maps proved by K. Astala [2] and answers in the positive a conjecture of K. Astala in op. cit.
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