Abstract
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.
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