文摘
The aim of this note is to construct a ψ-uniform domain G in the complex plane class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303730&_mathId=si1.gif&_user=111111111&_pii=S0022247X16303730&_rdoc=1&_issn=0022247X&md5=94bae88791bf8d066b81f41431841ecf" title="Click to view the MathML source">Cclass="mathContainer hidden">class="mathCode"> such that the identity mapping id: class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303730&_mathId=si2.gif&_user=111111111&_pii=S0022247X16303730&_rdoc=1&_issn=0022247X&md5=9d19c534d05cd0ef39c38d4bdb27aca7" title="Click to view the MathML source">(G,jG)→(G,kG)class="mathContainer hidden">class="mathCode"> is not an η-quasi-symmetric mapping for any homeomorphism η : class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303730&_mathId=si3.gif&_user=111111111&_pii=S0022247X16303730&_rdoc=1&_issn=0022247X&md5=e449ac4d1d286668c20091047921d056" title="Click to view the MathML source">[0,∞)→[0,∞)class="mathContainer hidden">class="mathCode">. This result shows that the answer to the related open problem, posed by Hästö, Klén, Sahoo and Vuorinen, is negative.