Hausdorff dimension of quasi-cirles of polygonal mappings and its applications |
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Authors: | ShengJin Huo ShuAn Tang ShengJian Wu |
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Affiliation: | 14458. LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, China 24458. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, 550001, China
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Abstract: | We show that the Hausdorff dimension of quasi-circles of polygonal mappings is one. Furthermore, we apply this result to the theory of extremal quasiconformal mappings. Let [µ] be a point in the universal Teichmüller space such that the Hausdorff dimension of f µ(?Δ) is bigger than one. We show that for every k n ∈ (0, 1) and polygonal differentials φ n , n = 1, 2, …, the sequence $ { [k_n frac{{overline {phi _n } }} {{|phi _n |}}]} $ cannot converge to [µ] under the Teichmüller metric. |
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