Quasiconformal mappings that highly distort dimensions of many parallel lines

Zoltán M. Balogh, Jeremy T. Tyson, Kevin Wildrick

Research output: Contribution to journalArticlepeer-review

Abstract

We construct a quasiconformal mapping of Rn, n ≥ 2, that simultaneously distorts the Hausdorff dimension of a nearly maximal collection of parallel lines by a given amount. This answers a question of Balogh, Monti, and Tyson.

Original languageEnglish (US)
Pages (from-to)61-72
Number of pages12
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Volume42
Issue number1
DOIs
StatePublished - 2017

Keywords

  • Dimension distortion
  • Foliation
  • Quasiconformal mapping
  • Sobolev mapping

ASJC Scopus subject areas

  • Mathematics(all)

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