Hausdorff dimension of quasi-cirles of polygonal mappings and its applications

作     者：HUO ShengJin TANG ShuAn WU ShengJian 

作者机构：LMAM and School of Mathematical SciencesPeking University School of Mathematics and Computer ScienceGuizhou Normal University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2013年第56卷第5期

页      面：1033-1040页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant Nos.10831004 and 11171080) 

主　　题：Hausdorff dimension Teichmiiller space quasi-circle polygonal mapping 

摘      要：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.