Doubling measures, monotonicity, and quasiconformality

Leonid V. Kovalev, Diego Maldonado, Jang Mei Wu

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel against doubling measures with suitable decay. The differentials of mappings that arise in this way satisfy an isotropic form of the doubling condition. We prove that this isotropic doubling condition is satisfied by the distance functions of certain fractal sets. Finally, we construct an isotropic doubling measure that is not absolutely continuous with respect to the Lebesgue measure.

Original languageEnglish (US)
Pages (from-to)525-545
Number of pages21
JournalMathematische Zeitschrift
Volume257
Issue number3
DOIs
StatePublished - Nov 2007

ASJC Scopus subject areas

  • Mathematics(all)

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