Mappings with convex potentials and the quasiconformal Jacobian problem

Leonid V. Kovalev, Diego Maldonado

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


This paper concerns convex functions that arise as potentials of quasiconformal mappings. Several equivalent definitions for such functions are given. We use them to construct quasiconformal mappings whose Jacobian determinants are singular on a prescribed set of Hausdorff dimension less than 1.

Original languageEnglish (US)
Pages (from-to)1039-1060
Number of pages22
JournalIllinois Journal of Mathematics
Issue number4
StatePublished - 2005
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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