Variation of quasiconformal mappings on lines

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

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
Volume195
Issue number3
DOIs
StatePublished - 2009

Keywords

  • Bounded variation
  • Generalized variation
  • Quasiconformal mappings
  • Quaternions

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Variation of quasiconformal mappings on lines'. Together they form a unique fingerprint.

Cite this