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 Teichmiille...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 Teichmiiller space such that the Hausdorff dimension of fμ（δ△） is bigger than one. We show that for every kn ∈ （0, 1） and polygonal differentials δn, n = 1, 2, the sequence {[kn δn/｜δn｜} cannot converge to [μ] under the Teichmiiller metric.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.10831004 and 11171080)
文摘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 Teichmiiller space such that the Hausdorff dimension of fμ（δ△） is bigger than one. We show that for every kn ∈ （0, 1） and polygonal differentials δn, n = 1, 2, the sequence {[kn δn/｜δn｜} cannot converge to [μ] under the Teichmiiller metric.
