Qusisymmetric dimension distortion of Ahlfors regular subsets of a metric space

Christopher J. Bishop, Hrant Hakobyan, Marshall Williams

We show that if $f:X\to Y$ is a quasisymmetric mapping between Ahlfors regular spaces, then ${\dim }_{H}f(E)\le {\dim }_{H}E$ for "almost every" bounded Ahlfors regular set $E\subseteq X$.…