Frequency of Sobolev and quasiconformal dimension distortion

@inproceedings{Balogh2010FrequencyOS,
  title={Frequency of Sobolev and quasiconformal dimension distortion},
  author={Zolt{\'a}n Balogh and Roberto Monti and Jeremy T. Tyson},
  year={2010}
}
We study Hausdorff and Minkowski dimension distortion for images of generic affine subspaces of Euclidean space under Sobolev and quasiconformal maps. For a supercritical Sobolev mapping f defined on a domain in R, we estimate from above the Hausdorff dimension of the set of affine subspaces parallel to a fixed m-dimensional linear subspace, whose image under f has positive H measure for some fixed α > m. As a consequence, we obtain new dimension distortion and absolute continuity statements… CONTINUE READING

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 63 references

A quasisymmetric surface with no rectifiable curves

  • C. J. Bishop
  • Proc. Amer. Math. Soc. 127,
  • 1999
Highly Influential
5 Excerpts

Sobolev spaces, dimension, and random series

  • R. Kaufman
  • Proc. Amer. Math. Soc. 128,
  • 2000
Highly Influential
14 Excerpts

On functions with derivatives in a Lorentz space

  • J. Kauhanen, P. Koskela, J. Malý
  • Manuscripta Math. 100,
  • 1999
Highly Influential
5 Excerpts

Reifenberg flat metric spaces, snowballs, and embeddings

  • G. David, T. Toro
  • Math. Ann. 315,
  • 1999
Highly Influential
4 Excerpts

Lusin’s condition (N) and mappings of the class

  • J. Malý, O. Martio
  • W . J. Reine Angew. Math
  • 1995
Highly Influential
4 Excerpts

The Gehring-Hayman inequality for quasihyperbolic geodesics

  • J. Heinonen, S. Rohde
  • Math. Proc. Cambridge Philos. Soc. 114,
  • 1993
Highly Influential
5 Excerpts

Hausdorff dimension and exceptional sets of linear transformations

  • R. Kaufman, P. Mattila
  • Ann. Acad. Sci. Fenn. Ser. A I Math. 1,
  • 1975
Highly Influential
4 Excerpts

Hausdorff dimension, orthogonal projections and intersections with planes

  • P. Mattila
  • Ann. Acad. Sci. Fenn. Ser. A I Math. 1,
  • 1975
Highly Influential
4 Excerpts

Similar Papers

Loading similar papers…