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 Teichmller spa...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 Teichmller space such that the Hausdorff dimension of fμ(Δ) is bigger than one.We show that for every kn∈(0,1) and polygonal differentials ψn,n=1,2,...,the sequence {[kn ψn/|ψn|]} cannot converge to [μ] under the Teichmer 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 Teichmller space such that the Hausdorff dimension of fμ(Δ) is bigger than one.We show that for every kn∈(0,1) and polygonal differentials ψn,n=1,2,...,the sequence {[kn ψn/|ψn|]} cannot converge to [μ] under the Teichmer metric.
