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}
}
  • C. Bishop, H. Hakobyan, M. Williams
  • 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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    SHOWING 1-10 OF 47 REFERENCES
    Geometric and analytic quasiconformality in metric measure spaces
    • 25
    • PDF
    Quasiconformality and quasisymmetry in metric measure spaces.
    • 81
    • PDF
    Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces
    • 8
    • PDF
    Sets of minimal Hausdorff dimension for quasiconformal maps
    • 35
    • Highly Influential
    • PDF
    Frequency of Sobolev and quasiconformal dimension distortion
    • 17
    • Highly Influential
    • PDF
    Conformal Dimension: Cantor Sets and Fuglede Modulus
    • 10
    • PDF
    Dimension of images of subspaces under Sobolev mappings
    • 9
    • PDF
    Dimension of images of subspaces under mappings in Triebel-Lizorkin spaces
    • 3
    • PDF