# Quasisymmetric dimension distortion of Ahlfors regular subsets of a metric space

@article{Bishop2012QuasisymmetricDD,
title={Quasisymmetric dimension distortion of Ahlfors regular subsets of a metric space},
author={C. Bishop and H. Hakobyan and M. Williams},
journal={Geometric and Functional Analysis},
year={2012},
volume={26},
pages={379-421}
}
• Published 2012
• Mathematics
• Geometric and Functional Analysis
• We show that if $${f\colon X\to Y}$$f:X→Y is a quasisymmetric mapping between Ahlfors regular spaces, then $${dim_H f(E)\leq dim_H E}$$dimHf(E)≤dimHE for “almost every” bounded Ahlfors regular set $${E\subseteq X}$$E⊆X. If additionally, $${X}$$X and $${Y}$$Y are Loewner spaces then $${dim_H f(E)=dim_H E}$$dimHf(E)=dimHE for “almost every" Ahlfors regular set $${E\subset X}$$E⊂X. The precise statements of these results are given in terms of Fuglede’s modulus of measures. As a corollary of these… CONTINUE READING
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