On the existence of harmonic mappings between doubly connected domains

Research output: Contribution to journalArticlepeer-review

Abstract

While the existence of conformal mappings between doubly connected domains is characterized by their conformal moduli, no such characterization is available for harmonic diffeomorphisms. Intuitively, one expects their existence if the domain is not too thick compared to the codomain. We make this intuition precise by showing that for a Dini-smooth doubly connected domain Ω* there exists a ε > 0 such that for every doubly connected domain Ω with ModΩ* < ModΩ < ModΩ* + ε there exists a harmonic diffeomorphism from Ω onto Ω*.

Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
DOIs
StateAccepted/In press - Apr 22 2018

Keywords

  • affine modulus
  • conformal modulus
  • doubly connected domain
  • harmonic mapping

ASJC Scopus subject areas

  • Mathematics(all)

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