A note on mappings preserving harmonic measure

Research output: Contribution to journalArticlepeer-review

Abstract

In this note we study mappings f preserving harmonic measures of boundary sets. We show that every homeomorphism f : D → Ω between Greenian domains D and Ω in Rn, n ≥ 2, preserving harmonic measures, is a harmonic morphism. We also study problems on conformality of mappings preserving harmonic measures of some specific sets on the boundaries of planar domains.

Original languageEnglish
Pages (from-to)2079-2089
Number of pages11
JournalProceedings of the American Mathematical Society
Volume148
Issue number5
DOIs
StatePublished - 2020

Keywords

  • Conformal mapping
  • Harmonic measure
  • Harmonic morphism

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