Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

Quasi-isometric and weakly quasisymmetric maps between locally compact non-complete metric spaces

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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