Bull. Korean Math. Soc. 2018; 55(3): 967-970
Online first article March 8, 2018 Printed May 31, 2018
https://doi.org/10.4134/BKMS.b170419
Copyright © The Korean Mathematical Society.
Xiantao Wang, Qingshan Zhou
Shantou University, Shantou University
The aim of this paper is to show that there exists a weakly quasisymmetric homeomorphism $f:(X, d)\to (Y, d')$ between two locally compact non-complete metric spaces such that $f:(X, d_h)\to (Y, d'_h)$ is not quasi-isometric, where $d_h$ denotes the Gromov hyperbolic metric with respect to the metric $d$ introduced by Ibragimov in $2011$. This result shows that the answer to the related question asked by Ibragimov in 2013 is negative.
Keywords: metric space, Gromov hyperbolic metric, weak quasisymmetric map, quasi-isometric map
MSC numbers: Primary 30F45; Secondary 53C23, 30C99
2018; 55(4): 1109-1124
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd