A note on the relationship between quasi-symmetric mappings and φ-uniform domains

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• 作者：Xiantao Wang^a ; ^{xtwang@stu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Qingshan Zhou^a ; ^{q476308142@qq.com" class="auth_mail" title="E-mail the corresponding author} ; Tiantian Guan^b ; ^{1548643494@qq.com" class="auth_mail" title="E-mail the corresponding author} ; Manzi Huang^b ; ^{mzhuang79@163.com" class="auth_mail" title="E-mail the corresponding author} ; Antti Rasila^c ; ^{antti.rasila@iki.fi" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Distance ratio metric ; Quasihyperbolic metric ; Uniform domain ; φ-uniform domain ; Quasi-symmetric mapping
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：1114-1119
• 全文大小：263 K

文摘

The aim of this note is to construct a ψ-uniform domain G   in the complex plane si1" class="mathmlsrc">si1.gif&_user=111111111&_pii=S0022247X16303730&_rdoc=1&_issn=0022247X&md5=94bae88791bf8d066b81f41431841ecf" title="Click to view the MathML source">C such that the identity mapping id: si2" class="mathmlsrc">si2.gif&_user=111111111&_pii=S0022247X16303730&_rdoc=1&_issn=0022247X&md5=9d19c534d05cd0ef39c38d4bdb27aca7" title="Click to view the MathML source">(G,j_G)→(G,k_G) is not an η-quasi-symmetric mapping for any homeomorphism η  : si3" class="mathmlsrc">si3.gif&_user=111111111&_pii=S0022247X16303730&_rdoc=1&_issn=0022247X&md5=e449ac4d1d286668c20091047921d056" title="Click to view the MathML source">[0,∞)→[0,∞). This result shows that the answer to the related open problem, posed by Hästö, Klén, Sahoo and Vuorinen, is negative.