Frequency of Dimension Distortion under Quasisymmetric Mappings

@inproceedings{Hakobyan2012FrequencyOD,
  title={Frequency of Dimension Distortion under Quasisymmetric Mappings},
  author={H. Hakobyan},
  year={2012}
}
We study the distortion of Hausdorff dimension of families of Ahlfors regular sets under quasisymmetric map f between metric spaces. We show that f cannot increase the dimension of “most” d-regular sets and we estimate the number of exceptional sets whose images have dimension ≥ d′ > d; the precise statements of both results involve modulus estimates for families of measures. For planar quasiconformal maps, the general estimates imply that if E ⊂ R is d-regular, then some component of f(E × R… CONTINUE READING

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