Variation of quasiconformal mappings on lines

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6 Scopus citations


We obtain improved regularity of homeomorphic solutions of the reduced Beltrami equation, as compared to the standard Beltrami equation. Such an improvement is not possible in terms of Holder or Sobolev regularity; instead, our results concern the generalized variation of restrictions to lines. Specifically, we prove that the restriction to any line segment has finite p-variation for all p > 1 but not necessarily for p = 1.

Original languageEnglish (US)
Pages (from-to)257-274
Number of pages18
JournalStudia Mathematica
Issue number3
StatePublished - 2009


  • Bounded variation
  • Generalized variation
  • Quasiconformal mappings
  • Quaternions

ASJC Scopus subject areas

  • General Mathematics


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