Quasi-isometric and weakly quasisymmetric maps between locally compact non-complete metric spaces
Bull. Korean Math. Soc. 2018 Vol. 55, No. 3, 967-970
Published online May 31, 2018
Xiantao Wang, Qingshan Zhou
Shantou University, Shantou University
Abstract : 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
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