Open AccessA note on mappings preserving harmonic measure
Author(s) -
Stamatis Pouliasis,
Alexander Yu. Solynin
Publication year - 2020
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/14870
Subject(s) - algorithm , artificial intelligence , annotation , computer science , database
In this note we study mappings f f preserving harmonic measures of boundary sets. We show that every homeomorphism f : D ¯ → Ω ¯ f:\overline {D}\to \overline {\Omega } between Greenian domains D D and Ω \Omega in R n \mathbb {R}^n , n ≥ 2 n\ge 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.