Frequency of Dimension Distortion under Quasisymmetric Mappings

  title={Frequency of Dimension Distortion under Quasisymmetric Mappings},
  author={H. Hakobyan},
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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Sets of Minimal Hausdorff Dimension for Quasiconformal Maps

View 4 Excerpts
Highly Influenced

Remarks on Sobolev imbedding inequalities

B. Bojarski
Complex analysis, Joensuu 1987, 52–68, Lecture Notes in Math. 1351, Springer, Berlin • 1988
View 6 Excerpts
Highly Influenced

Lectures on Analysis in Metric Spaces

J. Heinonen
Universitext. Springer-Verlag, New York • 2001
View 4 Excerpts
Highly Influenced

A remark on quasiconformal dimension distortion on the line

I. Prause
Ann. Acad. Sci. Fenn. Math. 32 • 2007
View 2 Excerpts

Ahlfors , Lectures on quasiconformal mappings

V. Lars

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