Weak quasisymmetry of homeomorphisms and homogeneity and Alhfors regularity of metric spaces Xiantao Wang (joint with Qingshan Zhou) Department of Mathematics, Shantou University, Shantou 515063, People's Republic of China Abstract. The main aim of this paper is to prove that a metric space is weakly quasisymmetrically equivalent to an Ahlfors regular space if and only if it is homogeneous with no isolated points. As an application, the open problem raised by Ibragimov in 2013 is negatively answered.