Smooth quasiregular maps with branching in Rn

Robert Kaufman, Jeremy T. Tyson, Jang Mei Wu

Research output: Contribution to journalArticlepeer-review

Abstract

According to a theorem of Martio, Rickman and Väisälä, all nonconstant C n/(n-2)-smooth quasiregular maps in Rn, n≥3, are local homeomorphisms. Bonk and Heinonen proved that the order of smoothness is sharp in R 3. We prove that the order of smoothness is sharp in R 4. For each n≥5 we construct a C 1+ε(n)-smooth quasiregular map in R n with nonempty branch set.

Original languageEnglish (US)
Pages (from-to)209-241
Number of pages33
JournalPublications Mathematiques de l'Institut des Hautes Etudes Scientifiques
Volume101
Issue number1
DOIs
StatePublished - Jun 2005

ASJC Scopus subject areas

  • Mathematics(all)

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