TY - JOUR
T1 - A note on the relationship between quasi-symmetric mappings and φ-uniform domains
AU - Wang, Xiantao
AU - Zhou, Qingshan
AU - Guan, Tiantian
AU - Huang, Manzi
AU - Rasila, Antti
N1 - Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - The aim of this note is to construct a ψ-uniform domain G in the complex plane C such that the identity mapping id: (G,jG)→(G,kG) is not an η-quasi-symmetric mapping for any homeomorphism η: [0,∞)→[0,∞). This result shows that the answer to the related open problem, posed by Hästö, Klén, Sahoo and Vuorinen, is negative.
AB - The aim of this note is to construct a ψ-uniform domain G in the complex plane C such that the identity mapping id: (G,jG)→(G,kG) is not an η-quasi-symmetric mapping for any homeomorphism η: [0,∞)→[0,∞). This result shows that the answer to the related open problem, posed by Hästö, Klén, Sahoo and Vuorinen, is negative.
KW - Distance ratio metric
KW - Quasi-symmetric mapping
KW - Quasihyperbolic metric
KW - Uniform domain
KW - φ-uniform domain
UR - http://www.scopus.com/inward/record.url?scp=84984806912&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2016.07.049
DO - 10.1016/j.jmaa.2016.07.049
M3 - 文章
AN - SCOPUS:84984806912
SN - 0022-247X
VL - 445
SP - 1114
EP - 1119
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -